Convocatoria de ayudas de Proyectos de Investigacion Fundamental no orientada

TECHNICAL ANNEX FOR TYPE A or B PROJECTS

1. SUMMARY OF THE PROPOSAL (the summary must be also filled in Spanish)

PROJECT TITLE: Dynamics associated to connections between invariant objects, astrodynamics, neu-roscience and other applications (DACOBIAN).

PRINCIPAL INVESTIGATOR: Amadeu Delshams

SUMMARY

(brief and precise, outlining only the most relevant topics and the proposed objectives):

The frame of the project is in the area of the Dynamical Systems and Applications. It is formed by arelatively numerous group of researchers, combining both senior experience and junior high projection,but making possible to embrace a wide spectrum of innovative applications with a same root. All thisthanks to, and based on, the development of an indispensable theoretical support.As for the objectives of the theoretical part, one seeks to advance in different aspects of Arnold diffusion,splitting of separatrices, study of bifurcations, computation of invariant objects and integrability. Inmany parts one will follow a computational approach, only possible by means of parallelization (thegroup owns a Beowulf cluster of high performance), to obtain results in Astrodynamics, Celestial Me-chanics, Quantum Mechanics, Particle Accelerators and Chemistry Physics. Although the group has abig experience and prestige in these fields, we remark as well the importance inside the project of novelapplications as Neuroscience, Strange Non Chaotic Attractors and Formation Flight of Satellites withsome EPO’s interested in the results.

TITULO DEL PROYECTO: Dinamica Asociada a Conexiones entre Objetos Invariantes, Astrodinamica,Neurociencia y otras Aplicaciones (DACOBIAN).

RESUMEN

(breve y preciso, exponiendo solo los aspectos mas relevantes y los objetivos propuestos):

El proyecto se enmarca dentro del area de los Sistemas Dinamicos y Aplicaciones. Esta formado porun grupo de investigadores relativamente numeroso, combinando a la vez experiencia y alta proyeccion,que hace posible abarcar un amplio espectro de aplicaciones punteras con una misma raız gracias, y enbase, al desarrollo de un soporte teorico indispensable.En cuanto a los objetivos de la parte teorica se preve avanzar en distintos aspectos de la difusion deArnold y la escision de separatrices, estudio de bifurcaciones, calculo de objetos invariantes e inte-grabilidad. En muchas partes se seguira un enfoque altamente computacional, solo posible medianteparalelizacion (el grupo dispone de un Beowulf cluster de altas prestaciones), para obtener resultados enAstrodinamica, Mecanica Celeste, Mecanica Cuantica, Aceleradores de Partıculas y en Quımica Fısica.Si bien el grupo tiene amplia experiencia y prestigio en estos ambitos, destacamos tambien la importan-cia dentro del proyecto de aplicaciones novedosas como Neurociencia, Atractores No Caoticos Extranosy vuelo en Formacion de Satelites con EPO’s interesadas en los resultados.

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2. INTRODUCTION(maximum 5 pages)

• The introduction should include: the aims of the project; the background and the state of the art of thescientific knowledge, including the essential references; the most relevant national and international groupsworking in the same or related topics.

2.1 Situation of the group and global purpose

The present project arises from the firm belief that dynamical systems are a way to understand nature,as well as a tool of analysis, interpretation and representation, accordingly to the the objectives presentedin the National Program of Mathematics of the present call. Not in vain, this project reflects a high degreeof interaction with sciences and technology. One of its strong points is, indeed, the transversality betweenapplications and theoretical studies, which has motivated much of the development of dynamical systemsthroughout history.

The project presents, in addition, a reasonable balance between the explotation of the expertise inthe field of dynamical systems and the exploration of new areas of research. About three fourths of theobjectives represent a continuation of the goals of previous projects, but the remaining fourth is noveland, therefore, more risky (for example, neuroscience, strange nonchaotic attractors, formation flightin constellations of satellites...). Nevertheless, this interest of the group in new subjects does not arisefrom anything: they have been acknowledged as important subjects in current science (astrodynamics,neuroscience, chemistry, theory of control, quantum mechanics, particle accelerators...) in which thegroup has been preparing for years, with a clear mission of multidisciplinarity and applicability of results.

This strategy is based on the wide experience and international recognition, both at a theoretical leveland in the applications of celestial mechanics, and a reputed network of collaborators for the developmentof the applications (see Section 4, on the methodology, and Section 6.0.5, on partner groups). Thanksto these collaborations, it has been possible to detect important problems in areas like astronomy andastrodynamics, neuroscience or physical chemistry in which the preparation of the group in dynamicalsystems may contribute decisively. l

At an organizational level, it is important to stress that this project can be considered as one of thefollow-ups of the coordinated project BFM2003-9504 between the UB and UPC. The splitting in twoindividual projects has several reasons: on one hand, the request of the group of the UB of a projectwithin the axis C, in which UPC group did not fit by restrictions of the call (5 previous projects ledby the MR); on the other hand, the remarkable growth of the UPC group in the last years, which hasbecome a pole of attraction of researchers and that has heightened its character as a coherent group witha sufficient critical mass. Besides, the components of the UPC of project BFM2003-07521 with a positionat UB have joined this project. All these incorporations contribute to reinforce and to extend diversescientific aspects of the previous project, as much at thematic level as in relation to the interconnections(see the table about interconnections in 4.5) or the connections with other external groups.

The existence of this wide and scientifically solid group has motivated a more ambitious project, whichis by no means a make-up to justify the numerical growth of the group. The reference to a sufficientcritical mass is often used in the call and we hope, therefore, that the size of the group is considered asa virtue and not simply penalized. In addition, we believe that it is more coherent not to split the teaminto subgroups, since the whole group shares similar topics, what leads a close collaboration in differentprojects between its members, as well as to a close methodology and experimental techniques.

Besides, this group has sufficient critical mass to carry out transversal activities, with multidisciplinargoals and real-world applications. In this sense, we emphasize the EPO’s DEIMOS and JPL/NASA,which are interested in the results of this project.

The composition of the group is, as well, balanced: on one hand, it grants expertise and, on the otherhand, a high level of projection. The group has 19 doctors, 5 of whom with shared dedication. Out of19 doctors, 8 are older than 40 years and 11 younger. The remaining 10 components (1 of which withshared dedication) are researchers in formation.

The group has grown since it has been able to attract, by means of competitive calls, several researchers(1 ICREA researcher, 2 “Ramon y Cajal” and 1 “Juan de la Cierva”) and 7 predoctoral students, all ofwhom hold a grant. All these have found in the group a suitable framework for formation and interactionwithin the different activities promoted by the group (Winter schools, thematic days, advanced courses,etc.), and within a quality PhD program, presently coordinated from the group (for more details, it seesection 7).

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On the other hand, there is a great interconnectivity of the objectives, as can be checked in the table ofthe section 4 about methodology and plan of work (the members of each one of the 14 proposed researchgoals participate, in average, in ten problems corresponding to the rest of goals), which gives a clear ideathat this it is a serious project, with foundations and a good cohesion.

Other remarkable indicators of quality are:

• The publishing activity of the group, both in quantity, with more than 120 ISI or MathSciNet publicationsfrom year 2000 and, mainly, in the quality of the journals (J. Nonlinear Sci., Comm. Math. Phys.,Phys. D, Memoirs. Amer. Math. Soc., Nonlinearity, Chaos, J. Differ. Equations, Adv. Math., etc.).Besides, more than 250 contributions to congresses have appeared , the group has received more than100 visitors and made more than 60 international visits and stays (see the background of the group formore detailed information). It is remarkable the increase in the publication of articles in high-impactjournals (in the first quartile in the classification of the JCR-Science in Mathematics and related areasand in MathSciNet) and articles in interdisciplinary journals.

• The present formation career, which has been quite successful. It has been able to attract young talentedresearchers both from Latin America and Europe.

• The obtention of finantial resources in competitive calls, coming from private institutions and pub-lic agencies like the Ministry of Education and Science, Autonomous Communities, European Union,NATO, etc. . . This includes basic research projects of type PROFIT, PETRI or similar and projects ofconsolidation of interdisciplinary groups. Moreover, solid international relations have been established bymeans of research projects and bilateral research programs (Spain-USA Commission, integrated actions)and through the coordination of European networks (INTAS).

• The solid contacts with the technological sectors (JPL/NASA, DEIMOS).

• The presence in several editorial boards, including 7 ISI journals, like Discrete Contin. Dynam. Systems(A. Delshams), Experiment. Math. (R. de la Llave), J. Math. Phys. (R. de la Llave), J. Nonlinear Sci.(A. Delshams), Nonlinearity (R. de la Llave), Rev. Math. Phys. (R. de la Llave) and SIAM J. Math.Anal. (R. de la Llave).

• The organization of many events, the coordination of the thematic network DANCE, the prizes received,the plenary talks at international conferences, the high number of cites to articles, the maintenance andupgrade of the parallel computing machine EIXAM (http://www.ma1.upc.edu/eixam/), as well as theposition of leadership in several research areas of dynamical systems (see Section 6 for more details aboutthis).

Concerning the project, the interest of the objectives proposed in Section 3 has been thoroughlyesteemed, trying to fit the statements to their expectations of success. The coherence of the plan ofcollaborations and visits was taken into account. The level of detail that offers the chronogram ofSection 4 makes it easy to appreciate in more detail the difficulty and convenience of the proposals. Theextrapolation of the number and the quality of the recent results and the present level of activity of thegroup allow to hold sufficent hope of continuity (see Section 5).

Once analyzed the position of the group in its scientific environment and exposed the global purposeof the project, we comment the highlights of the research project.

2.2 Background and present state of the scientific and technical developments

2.2.1 Invariant objects in dynamical systems and their connections

The study of Dynamical Systems, also known as “global analysis”, can be distinguished from alocal analysis by the interest to understand the phase portrait of a dynamical system for large times ofevolution and in a global way. Such study leads naturally to the consideration of the invariant objects,which vertebrate it and organize solutions around them.

The existence of invariant objects, the description of their properties and their approximation, bymeans of computational tools of numerical and symbolic analysis, along with their possible connections,presently constitute some of the most important lines of research in dynamical systems, both by itstheoretical interest and by its applicability to fields like astrodynamics.2.2.1.1 Invariant Objects and KAM theory

Among the most relevant invariant objects for the description of a dynamical system, there appear,firstly, fixed points or equilibrium points (depending wether time is discrete or continuous) and periodic

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and quasi-periodic orbits. For the study of the later, KAM (Kolmogorov-Arnold-Moser) methods arecommonly used, see the section by R. de la Llave in [151] for the present state-of-the-art and [8] for aretrospective vision.2.2.1.2 Integrability

Many of the methods referred in the previous paragraph for the construction of invariant objects,especially quasi-periodic trajectories, consider systems that are perturbations of integrable systems. Itis, thus, relevant to know the structure this type of systems, as well as the different formulations of thisconcept. At the same time, integrable systems are very rich and this makes their study interesting by itsown sake. A consequence of the transversal character of the group are the different points of view takenwhen approaching to the concept of integrability.

In Hamiltonian systems, the monograph by J.J. Morales [45] is still the reference work on algebraiccriteria for non-integrability. In this field there have been many developments since the approach, togetherwith J.-P. Ramis [175], of methods based on Differential Galois theory, see [177] and references therein.

Although many of the more prominent integrable systems are Hamiltonian,there is a wide class ofsystems which are not Hamiltonian (at least a priori), but that have an invariant measure in phase space,being in many cases integrable by means of quadratures. This topic has led to a renewed interst innon-holonomic mechanics [3, 154], which displays different characteristics from the Hamiltonian one.

Discrete integrable systems are another focus of interest, since the work of Veselov and Moser [47], whointroduced a discrete analog of the theorem of Liouville, and the discrete analogs of the Euler-Poincareand Lie-Poisson reduction [4, 40].2.2.1.3 Splitting of Separatrices

Frequently, hyperbolic invariant objects in integrable systems have connections or separatrices amongthem. When perturbing these systems, the connections are broken. This phenomenon is a mechanismfor the appearance of chaos, as well as for the existence of Arnold diffusion [1] in hamiltonianos with3 or more degrees of freedom. . The method of Poincare-Melnikov has proven to be useful to obtaincriteria for such splitting and has been widely developed within the group by A. Delshams, P. Gutierrez,R. Ramırez-Ros and T.M. Seara [19, 20, 21, 85], among others.

Nevertheless, the splitting and transversal intersection of the stable and unstable manifolds of ahyperbolic invariant object in a Hamiltonian system close to an integrable one is an exponentially smallphenomenon with respect to the perturbing parameter (see, for example, the survey by A. Delshamsand P. Gutierrez [88]). This makes it difficult to establish the validity of the method of Poincare–Melnikov, important for the existence of transverse homoclinic orbits. Besides this splitting gives rise tothe mechanism of transition chains, designed to detect the phenomenon of instability known as Arnolddiffusion [1] , for Hamiltonians with 3 or more degrees of freedom.

Complex variable and resummability techniques appear naturally in the computation of Poincare-Melnikov integrals. One of these techniques, with applications to the splitting of separatrices, is theso-called Ecale resurgence theory [24, 25, 26], developed by several French mathematicians includingthe group [ASD], starting from Borel resummability techniques for divergent series, and introduced inSpain by T.M. Seara and C. Olive [178]. Resurgence has proven to be very useful for the computationof separatrix splitting in dynamical systems close to integrable, since it allows to relate the existence of“analyzable” singularities, like poles or logarithmic singularities, to the appearance of exponentially smallphenomena. For a thorough exposition, see the survey by C. Olive, D. Sauzin and T.M. Seara [179], and[190].2.2.1.4 Arnold Diffusion

In the last years there has been a significant advance in the understanding of the mechanisms respon-sible for the so-called Arnold diffusion [1], which is an instability phenomenon for Hamiltonian systemswith more than two degrees of freedom. One of the main tools presently at hand is the scattering mapintroduced by A. Delshams, R. de la Llave and T.M. Seara, which has been applied to the proof, bygeometrical means, of the existence of orbits with unbounded energy in geodesic flows perturbed by aperiodic potential [92] (problem posed by J. Mather [42], see also [5]) as well as [94] for quasi-periodicperturbations . The monograph [95], where the existence of Arnold diffusion in a priori integrable systemsis proven, is nowadays the standard reference on geometrical methods for the instability in Hamiltoniansystems and has been used in other relevant contributions [10]. Indeed, the invited conference of R. dela Llave in the ICM2006 will be based on this subject.2.2.1.5 Bifurcations, Normal Forms and Computation of Invariant Objects

Very often dynamical systems are considered in parametric families. This leads to the study ofthe possible bifurcations that may happen in their dynamics. For instance in some relevant families,hyperbolicity is lost for some values of the parameters and this leads to the asymptotic analysis of the

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associated invariant manifolds, a study which began in [27]. When there is only partial hyperbolicity, thesituation can be even more complex [6].

To study bifurcations of the invariant objects, the use of normal forms is essential, not only in the“classical” Hamiltonian case [2, 9], but also in the reversible case [14, 84] o even without any symmetry.Besides, the method of normal forms can be used to obtain stability bounds [32, 16].

Although normal forms are generically divergent [50], in some situations they are not [46, 17]. Inothers, the introduction of a pseudo normal form [14] helps to study, through a convergent normal form,systems whose normal form diverges [90].

Nevertheless, the divergence of the normal form is not an obstacle to obtain a quantitative informationof the system, since by means of the control of its “speed of divergence” it is possible to get stability bounds[49, 32, 34], density of invariant objects [16, 34, 67, ?] and the size of the splitting of separatrices [27].2.2.1.6 Strange Nonchaotic Attractors

Dissipative systems appear in the modelling of natural phenomena and, unlike conservative systems,they can have attracting invariant objects. When such objects are not regular, we shall speak of strangeattractors which usually display chaotic dynamics, see [6] and, more generally, the results of the groups[IMPA] and [UOV]. However, in non-autonomous systems, such as quasi-periodically forced systems,the dynamics associated to the invariant object is not chaotic and we shall speak of strange nonchaoticattractors (SNA). These attractors, introduced for the first time in [58] show some particularities whichmakes the study of the experimental works in the literature interesting, both from a numerical andanalytical perspective.2.2.1.7 Return Maps

In recent results, the existence of isochronous manifolds around planar limit cycles has been linked toits hyperbolicity [11] and to the presence of Lie symmetries [52]. Also, in [28] these Lie symmetries havebeen related to its stability. The extension to higher dimensions is an interesting challenge which maylead to the control of isochronous manifolds. This is a problem in which the combination of theoreticaland numerical techniques may prove fruitful.

2.2.2 Astrodinamica

2.2.2.1 Formation flight of satellite constellationsSpace missions formed by a constellation of satellites have an increasing number of applications. Very

recently, formation flight of satellite constellations have emerged as a novel concept in space missions,both in ESA and NASA programs. Among the benefits of the use of such formations there are theimprovement of the precision of the instrumentation, the possibility of new scientific observations whichwere impossible with a single satellite, the robustness of the system, the reduction of costs . . .

In spite of its importance, the control of the formation flight of satellites is not completely solvedgenerically. Even simplest of the configurations, consisting of a pair of satellites on the same orbit aroundthe Earth, one following the other and keeping their mutual distance constant, the problem is difficultto generalize. Moreover, the existing solutions are obtained for precise configurations and after manynumerical analysis with ad hoc dedicated tools.2.2.2.2 Homoclinic and Heteroclinic connections for Solar System Navigation

The problem of the transfers between orbits is a classical subject in which the use of optimizationprocedures is the most common approach. Concerning the usage of the natural dynamics, and in par-ticular the consideration of invariant manifolds both for the transfer and interplanetary navigation, ourgroup, in collaboration with the UB group [UB] has published several reference surveys [127, 128, 131]and monographs [125, 126, 129]. These have opened new possibilities with a smaller fuel cost and aflexibility of superior design.

2.2.3 Mathematical and Computational Neuroscience

Neuroscience is one of the most rapidly growing fields in Liefe sciences which is getting significantfunding through public agencies. At the present stage of development, mathematics and computer scienceare crucial for the advance of neuroscience, and this has coined the terminology mathematical and compu-tational neuroscience. The starting point were differential equations and they continue to be a milestonefor the study of dynamical properties and rigorous proofs of experimental phenomena. Monographs like[13, 36, 37] show the growing theoretical body that has appeared in research articles like, for instance,[51].

2.2.4 Physical Applications

2.2.4.1 Quantum Mechanics

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Much of the methodology familiar to the components of the group may be used to approach problemsof quantum mechanics from similar points of view. A first approach based on the dynamical study of theeigenvalue equation of systems whose quantum Hamiltonian is one-dimensional. In the quasi-periodiccase, this approach has lead to the proof of several conjectures in the area like the “Aubry conjecture”or the “Ten Martini Problem” solved by J. Puig [184]. The use of algebraic techniques in integrabilityis also useful when looking for exact solutions for many-body problems [134]. In general, in many-bodyproblems, the analogy with the classical case is expected to give new insights.

2.2.4.2 Celestial Mechanics and Astronomy

Binary Asteroids: The dynamical evolution of binary asteroids provides a class of problems that can serveas fundamental models of more general rigid-body problems. Since the discovery, in 1993, of the firstnatural satellite of an asteroid, more than 50 binary asteroids have been identified [38]. The study of themotion of an artificial satellite around a binary asteroid is a subject of high relevance for the developmentof future missions to asteroids, since it is expected that a 16% of NEAs (Near Earth Asteroids) are binary[43].The problem of Trojans: The Trojan asteroids consist of two groups of asteroids, coorbital with Jupiter.These two groups cluster around two points that are known as the triangular (or Lagrange) points ofthe Sun-Jupiter system. Taking into account the influence of other planets, it is possible to constructmore realistic models. It is interesting to use semi-analytical techniques to study these new models, tocalculate invariant objects and to prove stability results. It is also important to make simulations inrealistic models and to use numerical tools (for instance frequency analysis) to give a better descriptionof the global structure of phase space.Galactic Dynamics: The enormous tails that emanate of some star conglomerates in orbit around ourgalaxy are due to stars that slide following invariant manifolds. These connect them with the deep space[12]. The computation of invariant objects (periodic orbits and tori) in galactic models is, therefore,important for the study of the formation of these “arms” and the transport of intergalactic material ingeneral.Horseshoe orbits in the Restricted Three-body Problem: The restricted three-body problem is one ofthe most popular models for the study of astronomical problems [54]. Although it has been widely studiedin the past, there remain many issues aspects to be analyzed. A deep understanding of this dynamics isvery important because, on one hand, it is widely used as a model in diverse planetary problems and, onthe other hand, it is a first step towards more complex models.Central configurations: The problem of finding the central configurations in a system of several bodiesin the plane subject to gravitational attraction has been studied in deepness in the last two hundredyears. In fact, its study has interest from the theoretical point of view, since these central configurationsare particular solutions of the problem of n bodies, and from the practical point of view, since thesesolutions are models for several problems in celestial mechanics (we mention, for example, the descriptionof Saturn rings, see [53, 48]).

2.2.4.3 Other applications

Particle Accelerators: The nonlinear effects of the dynamics of the particle accelerating beam can beimportant when studying the viability, design and construction of a compact electron michroton [44].More precisely, one would like to know the effects on the stability of the beam and the dynamic openingof the accelerator produced by sextupolar and octopolar magnets in synchrotron [30], as well as thenonlinear effects of the longitudinal dynamics of the beam in circuit michrotrons and their influence onthe acceptance of the accelerator.Molecular dynamics and chemical physics: The mechanisms of reaction by which reactants are combinedto form products are still little understood for most chemical reactions. Calculated rates of reaction bymeans of classical methods, like the Theory of State Transition (TST) [31, 55] may differ from theexperimentally observed ones by several orders of magnitude [15]. TST is based on the identification ofa state of transition between large regions of phase space, and assumes that each region does not havea particular structure [39]. Nevertheless, it is known that these regions do have a certain structure [33].Techniques based on the theory of dynamical systems are currently applied to the computation of rates ofchemical reactions, surpassing therefore the problems of TST, and taking into consideration the structureof homoclinic and heteroclinic connections in phase space [23, 56, 57, 29].

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2.3 Appendix: Bibliography prior to 2000 or external to members of the project

(to avoid unnecessary repetitions, the Bibliography of members of the project since 2000, as well as a list ofthe partner or similar research groups is in Section 6.0.5 of the Background of the applying group.)

[1] V.I. Arnol’d Instability of dynamical systems with many degrees of freedom Dokl. Akad. Nauk SSSR, 156:9–12,1964. 4

[2] V. I. Arnol’d Chapitres Supplementaires de la Theorie des Equations Differentielles Ordinaries Moscu: Mir(1980) 5

[3] A. M. Bloch. Nonholonomic mechanics and control. Springer-Verlag, New York, 2003. 4[4] A. Bobenko and Yu. B. Suris Discrete time Lagrangian mechanics on Lie groups, with an application to the

Lagrange top Comm. Math. Phys. 204:147–188, 1998. 4[5] S. Bolotin and D. Treschev Unbounded growth of energy in nonautonomous Hamiltonian systems Nonlinearity,

12:365–388, 1999. 4[6] C. Bonatti, L. Dıaz and M. Viana Dynamics beyond uniform hyperbolicity Encyclopaedia of Mathematical

Sciences, 102 Springer-Verlag, Berlin 2005. 5[7] C. Bonet, D. Sauzin, T.M. Seara and M. Valencia Adiabatic Invariant of the Harmonic Oscillator, Complex

Matching and Resurgence SIAM J. Math. An., 29 (6):1335–1360, 1998.[8] H. Broer KAM theory: the legacy of A. N. Kolmogorov’s 1954 paper. Bull. Amer. Math. Soc. (N.S.), 41(4):507–

521, 2004. 4[9] A. D. Bruno Local Methods in Nonlinear Differential Equations Berlın: Springer-Verlag (1989) 90c:58150 5

[10] C. Cheng and J. Yan, Existence of diffusion orbits in a priori unstable Hamiltonian systems J. Differential Geom.,67(3):457–517, 2004. 4

[11] C. Chicone, W. Liu. Asymptotic Phase Revisited, Journal of Differential Equations, 204: 227–246, 2004. 5[12] F. Combes, S. Leon and G. Meylan. N-body simulations of globular cluster tides. Astron. Astrophys., 352:149–162,

1999. 6[13] P. Dayan and L.F. Abbott. Theoretical neuroscience. MIT press, 2001. 5[14] D. DeLatte On normal forms in Hamiltonian dynamics, a new approach to some convergence questions Ergodic

Theory Dynam. Systems, 15:49–66, 1995. 5[15] N. De Leon. Cylindrical manifolds and reactive island kinetic theory in the time domain. J. Chem. Phys.,

96:285–297, 1992. 6[16] A. Delshams, P. Gutierrez, Estimates on invariant tori near an elliptic equilibrium point of a Hamiltonian system,

J. Differential Equations, 131:277–303, 1996. 5[17] A. Delshams, V. Gelfreich, A. Jorba, T.M. Seara, Exponentially small splitting of separatrices under fast quasiperi-

odic forcing, Comm. Math. Phys., 189:35–71, 1997. 5[18] A. Delshams, V. Gelfreich, A. Jorba, T.M. Seara, Lower and upper bounds for the splitting of separatrices of the

pendulum under a fast quasiperiodic forcing, ERA Amer. Math. Soc, 3:1–10, 1997.[19] A. Delshams, R. Ramırez-Ros, Poincare-Melnikov-Arnold method for analytic planar maps, Nonlinearity, 9, 1–26,

1996. 4, 26[20] A. Delshams, R. Ramırez-Ros, Melnikov potential for exact symplectic maps, Comm. Math. Phys., 190:213–45,

1997. 4, 26[21] A. Delshams, T.M. Seara, An asymptotic expression for the splitting of separatrices of the rapidly forced pendu-

lum. Comm. Math. Phys., 150(3):433–463, 1992. 4[22] A. Delshams, T.M. Seara, Splitting of separatrices in Hamiltonian systems with one and a half degrees of freedom.

Math. Phys. Electron. J. /, 3(1):1–40, 1997.[23] N. De Leon, M. A. Mehta, and R. Q. Topper. Cylindrical manifolds in phase space as mediators of chemical

reaction dynamics and kinetics. I. Theory. J. Chem. Phys., 94:8310–8328, 1991. 6[24] J. Ecalle Les Fonctions Resurgentes (Tomos I, II y III). Parıs: Publ. Math. d’Orsay (1981) 4[25] J. Ecalle Singularites non abordables par la geometrie Ann. Inst. Fourier (Grenoble), 52:73–164, 1992. 4[26] J. Ecalle Introduction aux Fonctions Analysables et Preuve Constructive de la Conjecture de Dulac Parıs:

Hermann, Actualites Math (1992) 4[27] E. Fontich, C. Simo, Invariant manifolds for near identity differentiable maps and splitting of separatrices, Ergodic

Theory Dynam. Systems, 10:319–46, 1990. 5[28] E. Freire, A.Gasull y A.Guillamon, Limit cycles and Lie symmetries, Preprint/CRM 584. 5, 26[29] F. Gabern, W.S. Koon, J.E. Marsden and S.D. Ross. Theory and Computation of Non-RRKM Lifetime Distri-

butions and Rates in Chemical Systems with Three or More Degrees of Freedom. Physica D, 211:391–406, 2005.6

[30] J. Gao. Analytical estimation of the dynamic apertures of circular accelerators, Nuclear Instruments and Methodsin Physics Research A, 451:545–557, 2000. 6, 17

[31] R. G. Gilbert and S. C. Smith. Theory of Unimolecular and Recombination Reactions. Blackwell Science Inc, firstedition, 1990. 6

[32] A. Giorgilli, A. Delshams, E. Fontich, L. Galgani, C. Simo, Effective stability for a Hamiltonian system near anelliptic equilibrium point, with an application to the restricted three-body problem, J. Differential Equations,77:167–98, 1989. 5

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[33] C. Jaffe, S. D. Ross, M. W. Lo, J. Marsden, D. Farrelly, and T. Uzer. Statistical Theory of Asteroid EscapeRates. Phys. Rev. Lett., 89(1):011101, 2002. 6

[34] A. Jorba y J. Villanueva, On the normal behaviour of partially-elliptic lower dimensional tori of Hamiltoniansystems. Nonlinearity, 10: 783–822, 1997. 5

[35] A. Jorba y J. Villanueva, On the persistence of lower dimensional invariant tori under quasi-periodic perturbations,Journal of Nonlinear Science, 7:427–473, 1997.

[36] J. Keener and Sneyd, J. Mathematical phisiology. Springer-Verlag, 1998. 5[37] C. Koch. Biophysics of computation Oxford University Press, 1999. 5[38] J. L. Margot et al. Binary Asteroids in the Near-Earth Object Population. Science, 296:1445–1448, 2002. 6[39] C. C. Marston and N. De Leon. Reactive islands as essential mediators of unimolecular conformational isomer-

ization: A dynamical study of 3-phospholene. J. Chem. Phys., 91:3392–3404, 1989. 6[40] J. E. Marsden, S. Pekarsky and S. Shkoller Discrete Euler-Poincare and Lie-Poisson equations Nonlinearity

12:1647-1662, 1999. 4[41] J.E. Marsden, S.D. Ross, New methods in celestial mechanics and mission design, Bull. Amer. Math. Soc. 43

(2006), 43–73. 26[42] J. N. Mather Graduate course at Princeton (no publicado) 4[43] W. J. Merline et al. Asteroids Do Have Satellites. Asteroids III , 289–312, 2002. 6[44] L. Michelotti. Intermediate classical dynamics with applications to beam physics, John Wiley & Sons Inc., New

York, 1995. 6[45] J. J. Morales-Ruız 1999 Differential Galois Theory and Non-Integrability of Hamiltonian Systems Basel:

Birkhauser Verlag 2000g:37076 4, 23, 25[46] J. K. Moser The analytic invariants of an area-preserving mapping near a hyperbolic fixed point Comm. Pure

Appl. Math.,9:673–92, 1956. 5[47] J. K. Moser and A. P. Veselov Discrete versions of some classical integrable systems and factorization of matrix

polynomials Comm. Math. Phys., 139:217-243, 1991. 4[48] C. D. Murray and S. F. Dermott. Solar system dynamics, Cambridge Press, 2000. 6[49] Nekhoroshev, N. N., An exponential estimate of the time of stability of nearly integrable Hamiltonian systems.

II, Trudy Sem. Petrovsk., 5: 5–50,1979. 5[50] R. Perez-Marco Convergence or generic divergence of the Birkhoff normal form Ann. of Math. (2) 157(2):557-574,

2003. 5[51] J. Rinzel and B. Ermentrout. Analysis of neural excitability and oscillations. Methods in Neural Modeling, Eds.

C. Koch and I. Segev, 135–169, 1989. 5[52] M. Sabatini. Isochronous sections via normalizers, International Journal of Bifurcation and Chaos, 15: 3031–3037,

2005. 5[53] H. Salo, C. F. Yoder. The dynamics of coorbital satellites systems. Astron. Astrophys., 205:309–327, 1988. 6[54] V. Szebehely. Theory of Orbits. Academic Press, 1967. 6[55] D. G. Truhlar, B. C. Garrett, and S. J. Klippenstein. Current Status of Transition-State Theory. J. Phys. Chem.,

100:12771–12800, 1996. 6[56] T. Uzer, C. Jaffe, J. Palacian, P. Yanguas, and S. Wiggins. The geometry of reaction dynamics. Nonlinearity,

15(4):957–992, 2002. 6[57] H. Waalkens, A. Burbanks, and S. Wiggins. Phase space conduits for reaction in multi-dimensional systems: HCN

isomerization in three dimensions. J. Chem. Phys., 121:6207–6225, 2004. 6[58] C. Grebogi, E. Ott, S. Pelikan and J.A. Yorke. Strange attractors that are not chaotic. Phys. D 13(1-2):261–268,

1984. 5

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3. OBJECTIVES(maximum 2 pages)

• 3.1 Describe the reasons to present this proposal and the initial hypothesis which support its objectives(maximum 20 lines)

Appropriateness of the research: At the present moment there is a reasonable baggage of results indynamical systems (topic area 8.3 of the National Program of Mathematics) and in some applicationswithin the group, mainly in celestial mechanics and astrodynamics. The results obtained so fare areof a theoretical nature as well as experimental, the latter based on numerical experiments. Most ofthe theoretical results have been obtained by means of constructive methods. This has influencedpositively the design and implementation of numerical computing tools, together with algorithms forthe computation of simple invariant objects. These includes semi-analytical methods containing thedevelopment of algebraic manipulators along with the corresponding calculation of the error. A specialemphasis has been put in trying parallelize the computations, in order to to take advantage of theparallel computing machine of the group, EIXAM (http://www.ma1.upc.edu/eixam/).In addition, the composition of the group, with 19 doctors and 10 researchers in formation, clusteredaround dynamical systems, makes it possible to tackle relevant problems and at the same time toapproach more novel ones, with a high degree of multidisciplinarity. This is aimed at fulfilling thedemands of research fields like astrodynamics, neuroscience, chemistry, theory of control, quantummechanics and particle accelerators, among others.

• 3.2. Indicate the background and previous results of your group or the results of other groups that supportthe initial hypothesis

As it has been mentioned in the introduction and appears in the section on the background of the group,we think that the group has a good publication level both in quantity and, mainly, in quality. This can beseen from the number of cites to the group articles, and the leadership position in several research areassuch as integrability, invariant objects and K.A.M. theory, conjugation, Poincare-Melnikov method,exponentially small splitting of separatrices, astrodynamics and celestial mechanics, both in analyticaland numerical tools.Some of the reference methods in the field, like the theory of Morales-Ramis, the scattering map, orthe real and complex parameterization of invariant manifolds, have been developed within the group,and have also been applied to realistic problems in astrodynamics. This theoretical and experimentalbaggage grants a good perspective of applicability in other fields.Last, but not least, the constant interaction between theory and numerical experimentation has beencrucial to validate the results.

• 3.3. Describe briefly the objectives of the project.

1. Invariant Objects in Dynamical Systems and their connections

(a) Arnold diffusion and Splitting of separatrices

Objectives: To prove the existence Arnold diffusion in systems close to integrable in biparametric fami-lies and to study of the properties of the associated scattering map, along with its effective computation.As applications related to Arnold diffusion, the study of nonpolynomial perturbations of Hamiltoniansystems and planar billiards with moving border. The study the splitting of separatrices associatedto a 3-dimensional invariant torus with “cubic” frequencies, the splitting of separatrices in reversiblesystems, the persistence of biasymptotic orbits of hyperbolic invariant curves, to extend the theory ofMorales-Ramis to the method of Poincare-Arnold-Melnikov, the splitting of separatrices in some singu-lar cases where the method of Poincare-Arnold-Melnikov is not applicable. The study of the resurgentformal solutions of a family of Hamilton-Jacobi equations.

(b) Bifurcations, normal forms and computation of invariant objects

Objectives: To study the bifurcations associated to the dynamics of the flat Poiseuille flow. Thedesign and implementation of parallel algorithms for the computation of normal forms and numericalmethods for the computation of rotation numbers of circle maps with high precision. To analyze thebreak-up of completely resonant maximal invariant tori of twist maps close to integrable. To studysome asymptotic properties and exponentially small phenomena related to the “ length spectrum ’ of

9

the strictly convex analytical curves. To obtain strange nonchaotic attractors in Harper maps. Tocontinue with the study of several aspects of the so-called “quasi-periodic Hopf bifurcation”. To analyzethe dynamics of linear symplectic quasi-periodic skew-products that appear in connection with quasi-periodic Schrodinger operators in a strip. To study geometric properties and invariant objects of discrete,Lagrangian and non-holonomic integrable systems.

(c) Integrability and return maps

Objectives: To prove to the non-integrability of certain N -body problems in Celestial Mechanics bymeans of the application of Morales-Ramis theory to the homothetic solutions. To study the differentnotions of integrability of a vector field through differential Galois theory, and to obtain connections withthe theory of Lie groups of symmetries. To describe all possible dynamics of billiards inside ellipsoidsof R3. To analyze the geometrical properties of the function given by the inversion of a hyperellipticalintegral. To study, for the planar polynomial vector fields, the inverse problem in integrability theory.To obtain results on return maps in relation with polynomial and planar vector fields with applicationsto the dynamics of limit cycles and isochronicity.

2. Astrodynamics

Objectives: To compute the reconfiguration of constellations using variational methods and the restrictedproblem as a model of motion. Determination of basic maneuvers for formations using variational methodsand realistic models of motion. Transfers of constellations of satellites in loose formation. The use ofadaptative methods to study the reconfiguration of constellations. The use of the homoclinical andheteroclinical connections for navigation in the Solar System. To analyze the transfer to the point ofLagrange L1 of the Earth-Moon system. To make a map of connections in the Solar System for navigationpurposes.

3. Mathematical and computational neuroscience

Objectives: To explain the appearance of bumps in the frequency spectrum of some experiments ofvisual stimulation. To apply mean-field techniques for the estimation of conductances at the visualcortex. To study the phenomenon of the synaptic depression. The modelling and analysis of activitypatterns and synchronization of neurons. The estimation of parameters from the dynamics of certaindynamical systems with applications in models of neuronal activity.

4. Physical applications

(a) Quantum mechanics, celestial mechanics and accelerators mechanics

Objectives: Analysis of the integrability of the Schrodinger equation through algebraic methods. Tocontinue with the dynamical methods of normal forms and reducibility in problems of spectral theory ofquasi-periodic Schrodinger operators. Numerical analysis of the Schrodinger operators with potentialsassociated to the invariant objects of twist maps. Study of the levels of energy of N bosons in animpenetrable sphere interacting through Coulomb repulsive forces. Applications of Arnold diffusionand hyperbolic phenomenology in the to the restricted three body problem. To study binary asteroidsdynamics and to continue with that of the Trojan asteroids. Proof of the existence of a finite number ofcentral configurations in the problem of 1+N bodies in the spatial case. To study of the effects nonlineardynamics in the particle accelerating beam. To study the formation of arms in barred galaxies and therole played by the invariant manifolds.

(b) Control theory and chemical physics

Objectives: To use the theory of averages and the bifurcations of codimension two in biparametricfamilies to the study of the power converters. To study problems of molecular dynamics and polyatomicisomerization by methods of invariant manifolds.To apply methods of attracting invariant manifolds tothe study of the kinetic models of the evolution of tropospheric ozone.

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4. METHODOLOGY AND WORKING PLAN(in the case of coordinated projects this title must include all the subprojects)

Detail and justify precisely the methodology and the working plan. Describe the working chronogram.

� The working plan should contain the tasks, milestones and deliverables. The projects carried out in theHesperides or in the Antarctic Zone must include the operation plan.

� For each task, it must be indicated the Centre and the researchers involved in it.

� If personnel costs are requested, the tasks to be developed by the personnel to be hired must be detailed andjustified. Remember that personnel costs are eligible only when personnel is contracted, fellowships are noteligible as personnel costs.

In each activity, one researcher is underlined as being in charge of the activity in the current project,and only for the researchers from other groups their affiliation is indicated, as in Section 6.0.5. Inparticular, in the case of activities carried out with other groups, the responsibility usually is shared, andthe outlined person denotes only responsibility within the components of the present project.

4.1 Invariant Manifolds in Dynamical Systems and their connections

4.1.1 Arnold Diffusion

[DD1] 18

A. Delshams, R. de la Llave and T.M. Seara will prove the existence of Arnold diffusion in systems closeto integrable in biparametric families. Afterwards. they will study the properties of the scattering mapassociated to normally hyperbolic invariant manifolds with an associated homoclinic manifold.

[DD2] 18

A. Delshams and P. Gutierrez will study the scattering map introduced in [92], approximating it by aMelnikov potential and finding the dominant harmonics, by using techniques similar to the ones developedin [87, 89].

[DD3] 18

A. Delshams and P. Roldan will work in a numerical method to effectively compute the scattering map[92] associated to normally hyperbolic invariant manifolds to check numerically the existence of diffusionin Hamiltonian systems.

[DD4] 18

A. Delshams and G. Huguet will work in the big gaps problem in Arnold diffusion [95] for non-polynomialperturbations of a priori unstable Hamiltonian systems.

[DR1] 18

R. de la Llave and R. Ramırez will study the existence of orbits with unbounded velocity in planarbilliards with a moving boundary.

4.1.2 Splitting of separatrices and Resurgence theory

[RD1] 18

A. Delshams and P. Gutierrez, with O. Koltsova y L. Lerman [RIAMC], will study the dynamics ofHamiltonian reversible systems close to homoclinic connections of multisaddle-multicentre equilibriumpoints, generalizing the results obtained in [152] on splitting of separatrices of invariant tori close to ahomoclinic loop of a center-center-saddle.

[RD2] 18

A. Delshams and P. Gutierrez plan to study the splitting of separatrices associated to a 3-dimensionalinvariant torus with cubic frequencies, generalizing the analytical and numerical tools developed for 2-dimensional tori with quadratic frequencies in [86]. This study could also be used as a tool to face openproblems in 3 degrees-of-freedom KAM theory.

11

[RD3] 18

A. Delshams, V. Gonchenko [RIAMC] and J.T. Lazaro plan to study the existence of “mixed dynamics”in reversible systems with a reversible homoclinic tangency. The idea is to show the existence of systemswhere an infinite amount of periodic points of elliptic type, saddle type, stable, unstable coexist; and,also with regions of Newhouse type.

[RD4] 18

S. Bolotin [MSU], A. Delshams, Yu. Fedorov and R. Ramırez had proved the persistence of biasymptoticorbits to hyperbolic periodic orbits of elliptic billiards [83, 66]. To continue with this work, they willstudy the persistence of biasymptotic orbits to hyperbolic invariant curves. To this end, the expressionof the dynamics on the invariant manifolds of the point [IR1] will be needed.

[RG1] 18

P. Gutierrez and J.T. Lazaro plan to extend the known results on splitting of separatrices and transver-sal homoclinic orbits for the Hamiltonian case, to reversible systems, establishing a comparative studybetween the two types of systems.

[RM1] 18

J.J. Morales and J.-P. Ramis [UPS] intend to extend the Morales-Ramis theory to the Poincare-Arnold-Melnikov method. They want to prove that the component of the identity of the Galois group of thevariational equation along the invariant manifolds of an integrable Hamiltonian system must be commu-tative. As a corollary, they may give a perturbative version of the Poincare-Arnold-Melnikov method inthis context.

[RR1] 18

R. Ramırez has recently published [187], a numerical study on the exponentially small splitting of sepa-ratrices in billiards inside perturbed circunferences. Now, with P. Martın and T.M. Seara, they will tryto prove analytically some of the results.

[RS1] 18

I. Baldoma [UB] and T.M. Seara will prove the existence of Silnikov-type bifurcations in analytic unfold-ings of the central singularity in R3.

[RS2] 18

I. Baldoma [UB], E. Fontich [UB], C. Olive and T.M. Seara will compute the asymptotic splitting ofseparatrices of periodically perturbed planar systems in the singular case, where the Melnikov theorydoes not hold.

[RS3] 18

P. Martın, D. Sauzin [ASD] and T.M. Seara will use “matching” techniques and “resurgence” in theasymptotic calculation of the area of the lobes between homoclinic intersections for “big” perturbationsof the MacMillan map. They will also prove the existence of “resurgent solutions”.

[RS4] 18

C. Olive and T.M. Seara will measure the exponentially small splitting of separatrices produced in Hamil-tonian systems with a “big” and “fast” perturbation. They will use “matching” techniques in the complexplane and “resurgence” theory.

[RS5] 18

C. Olive, D. Sauzin [ASD] and T.M. Seara will construct the formal general integral in a Hamilton-Jacobiequation depending on a new suitable parameter and they will study its convergence. In addition to the“resurgence” theory, they plan to use numerical tools.

4.1.3 Integrability

[IG1] 18

F. Calogero [URLS], D. Gomez-Ullate, P. Santini [URLS] and M. Sommacal [UP6] will study a new modelof transition to chaos based on the analysis of the evolution in real time of a dynamical system consideredas a path on a complex Riemannian surface.

12

[IG2] 18

Y. Fedorov and D. Gomez-Ullate will study the geometrical properties of the complex solutions of animportant class of integrable systems that can be reduced to the inversion of a hyperelliptic integral.These solutions have an infinite number of branch points and their projection is dense in the complexplane.

[IM1] 18

J.J. Morales and S. Simon [UB] will study the non-integrability of some N-body problems in CelestialMechanics using differential Galois theory. More precisely, they will focus on problems of central config-urations, using as a main tool Morales-Ramis theory.

[IM2] 18

D. Blazquez [UB] and J.J. Morales will study several notions of integrability of vector fields by means ofdifferential Galois theory. In particular, they want to analyze the connections between the existence ofLie symmetry groups and the Galois group. Together with C. Pantazi, they will study the possibility ofapplying the former to specific cases of polynomial fields.

[IP1] 18

J. Llibre [UAB] and Ch. Pantazi will study, for polynomial fields in the plane, the inverse problem of in-tegrability theory and they will investigate the connection of integrability with the concept of multiplicityof invariant curves.

[IR1] 12, 18

Y. Fedorov and R. Ramırez will describe all possible dynamics of billiards in ellipsoids of R3. Thereare already explicit formulas for the generic dynamics in terms of hyperelliptic functions and for thedynamics on the invariant manifolds of the hyperbolic periodic orbits in terms of tau functions. Theyaim at obtaining explicit representations of other type of dynamics.

4.1.4 Bifurcations, normal forms and computation of invariant objects

[BC1] 19

P.S. Casas, jointly with the group [FA], will study the dynamics of the Poiseuille planar flow. The aimis to complete the computation of periodic and quasi-periodic solutions to a broader range of Reynoldnumbers and waves, the bifurcations to other solutions, the connections between them and their stability.Afterwards, and taking as starting point the results for dimension two, they will perform a similar studyin dimension three and construct an efficient numerical integrator that can be implemented in a Beowulfcluster.

[BD1] 19

A. Delshams, R. de la Llave and P. Roldan will design and implement new parallel algorithms for thecomputation of normal forms in clusters.

[BM1] 19

E. Fontich [UB], R. de la Llave, and P. Martın will study the existence and decay properties of invariantmanifolds associated to hyperbolic sets of weakly coupled lattice maps. They will also prove theoremson the conjugacy of the dynamics on these sets.

[BM2] 19

I. Baldoma [UB], E. Fontich [UB], R. de la Llave and P. Martın will study the existence and regularityof 1-dimensional invariant manifolds associated to parabolic points.

[BO1] 19

During the last years, M. Olle, J.R. Pacha and J. Villanueva have been working in several aspects ofthe “quasiperiodic Hopf bifurcation” for periodic orbits of Hamiltonian systems with three degrees-of-freedom, by means of normal form techniques, KAM theory and numerical methods [180, 181, 182]. Theywill continue to obtain new results on the topic.

[BP1] 19

A. Haro [UB] and J. Puig will show how strange nonchaotic attractors appear in Harper type maps, andthey will later generalize the results to higher dimensions.

13

[BP2] 19

A. Haro [UB] and J. Puig will study the dynamics of the linear symplectic quasiperiodic skew-productsthat appear related to quasiperiodic Schrodinger operators in a strip. In analogy with the 1-dimensionalcase [184], it is believed that some open problems in spectral theory might be settled in this way.

[BR1] 19

R. Ramırez will analyze the splitting of completely resonant maximal invariant tori of twist maps closeto integrable. The first part, published in [188] focused in the planar case, and the theory developedto study billiards inside a circumference was applied. In a second phase, together with A. Delshamsand V. Rothos (Loughborough Univ), they will study the case of perturbed ellipses, which requires moresophisticated tools. Finally, they plan to extend the theory to the multidimensional case and to apply itto perturbed ellipsoids.

[BR2] 19

R. Ramırez will study some asymptotic properties and exponentially small phenomena associated to thelength spectrum of strictly convex analytic curves.

[BV1] 19, 23

A. Luque, T.M. Seara and J. Villanueva will work in a numerical method for the computation of rotationnumbers of circle maps with high precision. Later on, they will generalize this method to a severalother contexts: rotation vectors of n-dimensional tori, computation of the “size” of the Herman rings,computation of invariant tori, frequency analysis, etc.

4.1.5 Return and Time maps associated to low dimensional objects

[AG1] 19

A. Guillamon and Ch. Pantazi are studying the phase portraits and the period function of Hamiltoniansof the form H(x, y) = F (x) +G(y), where F and G are polynomials.

[AG2] 19

A. Guillamon and G. Huguet will work in the effective computation of isochronous sections by means ofLie symmetries, aiming at applying it to the study of biological clocks and to the stability of limit cyclesand other invariant objects.

[AG3] 19

A. Gasull [UAB] and A. Guillamon will study limit cycles in generalizations of the Abel equation.

[AG4] 19

A. Guillamon and M. Sabatini (Univ. of Trento) will work on a general method to study the stabilityproblem of limit cycles using Lie symmetries.

[AL1] 19

J.T. Lazaro and J. Torregrosa [UAB] have started the study of isochronicity conditions in families ofpolynomials in the plane with the intention to apply this to the center-focus problem. They will alsolook for a unified treatment of the Lyapunov constants (associated to a linear saddle) and the “saddlequantities”, observed in a saddle point.

[AP1] 19

J. Llibre [UAB] and Ch. Pantazi will study the periodic orbits in polynomial systems in dimension threewith certain type of symmetries, and will investigate their number of limit cycles.

4.2 Astrodynamics

4.2.1 Satellite formation flight

[VM1] 19

L. Garcıa and J. Masdemont will work on the reconfiguration of satellite constellations using variationalmethods and the restricted three body problem as the model for the motion.

14

[VM2] 19

L. Garcıa and J. Masdemont will study the problem of determining basic maneuvers for formation flightwith variational methods and realistic models of motion.

[VM3] 19

G. Gomez [UB], J. Masdemont and M. Marcote [UB] will study the transfers of satellite constellationsin lax formation.

[VM4] 19

L. Garcıa and J. Masdemont will use adaptive methods to study constellation reconfiguration using therestricted three body problem as the model for the motion.

4.2.2 Homoclinic and heteroclinic connections for the navigation in the Solar System

[CoM1] 19

E. Canalias, A. Delshams, J. Masdemont, J.M. Mondelo [UAB] and P. Roldan will study the homoclinicand heteroclinic connections of low order in the restricted three body problem.

[CoM2] 19

E. Canalias, G. Gomez [UB], M. Marcote [UB], J. Masdemont and J.M. Mondelo [UAB] will study thehomoclinic and heteroclinic connections of low order in coupled problems of four bodies.

[CoM3] 19

G. Gomez [UB], J. Masdemont and J. Mondelo [UAB], will use the connection map, mentioned in [SM1]to explain the natural transport mechanisms of material in the Solar System beyond the Kuiper belt.

4.2.3 Navigation software and orbit generation

[SM1] 15, 19

J. Masdemont and E. Canalias plan to study the transfers to L1 of the Earth-Moon system.

[SM2] 19

G. Gomez [UB], J. Masdemont and J.M. Mondelo [UAB] will generate, in the most precise possible form,a connection map to navigate in the Solar System.

4.3 Computational and Mathematical Neuroscience

[NG1] 20

A. Guillamon and L. Tao [NYU] intend to explain the appearance of “bumps” in the frequency spectrumof some visual stimulation experiments with “drifting gratings”. They will use neuronal models withparameters close to Bogdanov-Takens bifurcations.

[NG2] 20

A. Guillamon and L. Tao [NYU] will apply mean-field techniques to estimate conductances of the visualcortex. This work requires to deal with stochastic differential equations and, thus, it is proposed as amid-term objective. This is related to the work of professors D. McLaughlin [NYU] and J. Rinzel [NYU].

[NG3] 20

J.M. Benita, G. Deco [UPF], A. Guillamon and M.V. Sanchez-Vives [UMH] will study, from a theoreticalpoint of view, the phenomenon of (short-term depression) under different regimes of cortex stimulation.

[NG4] 20

J.P. Francoise [UP6], D. Gomez-Ullate and A. Guillamon will work on inverse problems in dynamicalsystems, that is, the estimation of parameters from the dynamics of the system. To this end, they willstudy local expansions of the state variables (or associated functions) near bifurcations that generatelimit cycles. The work is oriented towards applications in estimating parameters of models of neuronalactivity.

15

[NH1] 20

G. Huguet and D. Terman [OSU] will work on the modelling and analysis of activity patterns and neuronalsynchronization in the pre-Botzinger region in the brain.

4.4 Physical Applications

4.4.1 Celestial Mechanics

[CeD1] 20

E. Canalias, A. Delshams, J. Masdemont and P. Roldan will investigate the applications of methods forthe computation of Arnold diffusion trajectories (normally hyperbolic invariant manifolds and scatteringmaps to the three body problem, in the planar and spatial cases.

[CeG1] 20

F. Gabern, W.S. Koon [CAL], J.E. Marsden [CAL] and D.J. Scheeres (U. Michigan) will work on thestudy of the dynamics of binary asteroids. Asteroid pairs are a canonical model for more general rigid-body problems. To study its dynamics and the motion of a satellite nearby, they will use geometricmechanics methods combined with numerical tools based on dynamical systems theory.

[CeG2] 20

F. Gabern, A. Jorba [UB], U. Locatelli [UROM] and P. Robutel [ASD] will contine to study the problemof the stability of Trojan asteroids. They propose to use a combination of numerical and semi-analyticaltechniques with new theoretic developments to improve the current results.

[CeM1] 20

A. Athanassoula [ObM], J. Masdemont and M. Romero (URV) will use methods from astrodynamics tostudy galactic dynamics, like the computation of invariant objects (periodic orbits and tori) for the studyof arm formation and material transport.

[CeO1] 20

E. Barrabes [UB] and M. Olle will study different types of horseshoe orbits: periodic, quasiperiodic andhomoclinic in the restricted three body problem (in its variants: planar or spatial and circular or elliptic).They will also consider applications to the co-orbitals of Saturn.

[CeO2] 20

J.M. Cors [UAB], J. Llibre [UAB] and M. Olle will study the conjecture on the existence of a finitenumber of central configurations in the n-body problem and, more precisely, when n = 1 + N in thespatial case. They will use analytical and numerical methods.

[CeO3] 20

E. Barrabes [UB], J.M. Mondelo [UAB] and M. Olle aim at globalizing the phase space portrait near theL3 collinear equilibrium point of the restricted three body problem. They will begin with the globalizationof the stable and unstable manifolds of the central manifold of L3, by using numerical, analytical or semi-analytical methods.

4.4.2 Quantum mechanics

[CuG1] 20

D. Gomez-Ullate, N. Kamran [UMG] and R. Milson [UMG] will study exact solutions of the Schrodingerequation for models of several interacting bodies, by using algebraic methods, like for instance Darbouxtransformation or quasi-exact solvability.

[CuM1] 20

P. Acosta-Humanez and J.J. Morales will study the integrability of the Schrodinger equation by meansof differential Galois theory. In particular, they want to study the Darboux transformation by means ofthe Picard-Vessiot theory.

16

[CuP1] 20

H. Broer [RUG] and J. Puig will work on the diffusion of dynamical methods of normal forms and re-ducibility problems of spectral theory of quasiperiodic Schrodinger operators, as it was already startedin [68]. Jointly with C. Simo, they will study numerically (using parallel computing) spectral prob-lems with several frequencies and will analyze afterwards some conjectures in the field of quasiperiodicSchrodinger operators. Jointly with R. Johnson [UFI], they will try to apply recent results to the studyof KdV equations.

[CuP2] 20

J. Puig will study numerically Schrodinger operators with potentials associated to invariant objects oftwist maps, with the aim to explain, later on, criteria like Greene’s one.

[CuV1] 20

J. Villanueva and J. Haro [GRED] will study the energy levels of N bosons in an impenetrable sphereinteracting by means of Coulomb forces, by using the Hartree approximation. Their intention is tocombine analytical and numerical methods.

4.4.3 Control Theory

[TS1] 20

F. Angulo and E. Fossas [IOC] jointly with T.M. Seara will apply averaging theory to the regularizationof power converters, where control techniques of zero mean dynamics are used, and they will obtainpredictions of the output error and of the sliding surface.

[TS2] 20

F. Angulo, M. di Bernardo, E. Fossas, S.J. Hogan and G. Olivar [IOC], jointly with T.M. Seara will studybifurcations of codimension two in biparametric families of non-regular dynamical systems on the planethat model the dynamics of power converters.

4.4.4 Particle Accelerators

[PS1] 20

O. Larreal, A. Luque, P. Martın, T.M. Seara and J. Villanueva, jointly with Y. Kubyshin [INTE], willstudy the nonlinear effects of the dynamics of the beam in particle accelerators produced by sextupole andoctupole magnets in synchrotrons, and the nonlinear effects of the longitudinal beam in circuit microtronstogether with its influence on the accelerator [30].

4.4.5 Chemical Physics

[QG1] 20

F. Gabern, W.S. Koon [CAL], J.E. Marsden [CAL] and T. Yanao [CAL] will study molecular dynamicsand polyatomic isomerization problems. The goal is to advance in the theory and computations ofchemical reaction rates by means of theoretical and computational methods based on dynamical systemstheory and invariant manifolds.

[QV1] 20

A. Luque and J. Villanueva will study kinetic models of the evolution of tropospheric ozone by means ofthe computation of normal forms and the reduction of the dynamics to attracting invariant manifolds.

17

4.4 CHRONOGRAM MODEL (EXAMPLE)This chronogram must indicate the persons involved in the project, including those contracted with projectfunds.Underline the name of the person responsible of each task.

Invariant Objects Chronogram

Tasks Centre Persons First year (*) Second year (*) Third year (*)

[DD1] UPC Delshams, Llave, Seara

[DD2] UPC Delshams, Gutierrez

[DD3] UPC Delshams, Roldan

[DD4] UPC Delshams, Huguet

[DR1] UPC Llave, Ramırez

[RD1] UPC Delshams, Gutierrez,Koltsova [RIAMC],Lerman [RIAMC]

[RD2] UPC Delshams, Gutierrez

[RD3] UPC Delshams, Gonchenko[RIAMC], Lazaro

[RD4] UPC Bolotin [MSU], Delshams,Fedorov, Ramırez

[RG1] UPC Gutierrez, Lazaro

[RM1] UPC Morales, Ramis [UPS]

[RR1] UPC Martın, Ramırez, Seara

[RS1] UPC Baldoma [UB], Seara

[RS2] UPC Baldoma [UB], Fontich[UB], Olive, Seara

[RS3] UPC Martın, Sauzin [ASD],Seara

[RS4] UPC Olive, Seara

[RS5] UPC Olive,Sauzin[ASD], Seara

[IG1] UPC Calogero [URLS], Gomez-Ullate, Santini [URLS],Sommacal [UP6]

[IG2] UPC Fedorov, Gomez-Ullate

[IM1] UPC Morales, Simon [UB]

[IM2] UPC Blazquez [UB], Morales,Pantazi

[IP1] UPC Llibre [UAB], Pantazzi

[IR1] UPC Fedorov, Ramırez

18

Invariant Objects Chronogram (continued)

Tasks Centre Persons First year (*) Second year (*) Third year (*)

[BC1] UPC Casas

[BD1] UPC Delshams, Llave, Roldan

[BM1] UPC Fontich[UB],Llave,Martın

[BM2] UPC Baldoma [UB], Fontich[UB], Llave Martın

[BO1] UPC Olle, Pacha, Villanueva

[BP1] UPC Haro [UB], Puig

[BP2] UPC Haro [UB], Puig

[BR1] UPC Ramırez

[BR2] UPC Ramırez

[BV1] UPC Luque, Seara, Villanueva

[AG1] UPC Guillamon, Pantazi

[AG2] UPC Guillamon, Huguet

[AG3] UPC Gasull [UAB], Guillamon

[AG4] UPC Guillamon, Sabatini

[AL1] UPC Lazaro, Torregrosa [UAB]

[AP1] UPC Llibre [UAB], Pantazi

Astrodynamics Chronogram

Tasks Centre Persons First year (*) Second year (*) Third year (*)

[VM1] UPC Garcıa, Masdemont

[VM2] UPC Garcıa, Masdemont

[VM3] UPC Gomez [UB], Masdemont,Marcote[UB]

[VM4] UPC Garcıa, Masdemont

[CoM1] UPC Canalias, Delshams, Mas-demont, Mondelo [UAB],Roldan

[CoM2] UPC Canalias, Gomez [UB],Marcote[UB],Masdemont,Mondelo [UAB]

[CoM3] UB Gomez [UB], Masdemont,Mondelo [UAB]

[SM1] UPC Canalias, Masdemont

[SM2] UB Gomez [UB], Masdemont,Mondelo [UAB]

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Mathematical and Computational Neuroscience

Tasks Centre Persons First year (*) Second year (*) Third year (*)

[NG1] UPC Guillamon, Tao [NYU]

[NG2] UPC Guillamon, Tao [NYU]

[NG3] UPC Benita, Deco [UPF], Gui-llamon, Sanchez [UMH]

[NG4] UPC Francoise [UP6], Gomez-Ullate, Guillamon

[NH1] UPC Huguet, Terman [OSU]

Physics Applications

Tasks Centre Persons First year (*) Second year (*) Third year (*)

[CeD1] UPC Canalias, Delshams,Masdemont, Roldan

[CeG1] UPC Gabern, Koon [CAL],Marsden [CAL], Scheeres

[CeG2] UPC Gabern, Jorba [UB], Lo-catelli [UROM], Robutel[ASD]

[CeM1] UPC Athanassoula [ObM],Masdemont, Romero

[CeO1] UPC Barrabes [UB], Olle

[CeO2] UPC Cors & Llibre [UAB], Olle

[CeO3] UPC Barrabes [UB], Mondelo[UAB], Olle

[CuG1] UPC Gomez-Ullate, Kamran[UMG], Milson [UMG]

[CuP1] UPC Broer [RUG], Johnson[UFI], Puig, Simo [UB]

[CuP2] UPC Puig

[CuV1] UPC Villanueva, Haro [GRED]

[CuM1] UPC Acosta, Morales

[TS1] UPC Angulo and Fossas [IOC],Seara

[TS2] UPC Angulo, Bernardo,Fossas, Hogan y Olivar[IOC], Seara

[PS1] UPC Larreal, Luque, Martın,Seara, Villanueva,Kubyshin [INTE]

[QG1] UPC Gabern, Koon, Marsden yYanao[CAL]

[QV1] UPC Luque, Villanueva(*) Mark an X inside the corresponding boxes (months)

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4.5 TABLE OF INTERCONNECTIONIn the way this section has been developed, the research of the group is distributed in 14 great subjects

(4.1.1, . . . , 4.4.5). Through an objective value which we have called interconnectivity degree (γ), in Table1 there appears a very positive characteristic of the group: the collaboration between its members andthe high degree of intersection between people who dedicate themselves to different subjects. Note thatthe values are really high, with an average of 10 collaborations by subject; that is to say, the members ofeach subject participate in ten problems corresponding to other subjects.

4.1.1 4.1.2 4.1.3 4.1.4 4.1.5 4.2.1 4.2.2 4.2.3 4.3 4.4.1 4.4.2 4.4.3 4.4.4 4.4.5 γ

4.1.1 (7) 4 1 5 1 0 1 0 1 2 0 1 1 0 174.1.2 (9) 3 4 1 0 1 0 0 1 1 1 2 0 184.1.3 (5) 1 1 0 0 0 1 0 2 0 0 0 94.1.4 (12) 0 0 1 0 0 3 2 1 4 2 234.1.5 (4) 0 0 0 2 0 0 0 0 0 54.2.1 (2) 1 1 0 1 0 0 0 0 34.2.2 (3) 2 0 3 0 0 0 0 94.2.3 (2) 0 2 0 0 0 0 54.3 (4) 0 1 0 0 0 5

4.4.1 (6) 0 0 0 1 134.4.2 (5) 0 1 1 84.4.3 (1) 1 0 44.4.4 (5) 2 114.4.5 (3) 6

Table 1: Table of interconnectivity: The values between parenthesis represent the number of individualsthat works in each subject; the other values represent the people who dedicate themselves simultaneouslyto both subjects that intersect in that square. The last column reflects the sum of participations in othersubjects of members of the subject that heads the respective row.

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5. BENEFITS DERIVED FROM THE PROJECT, DIFFUSION AND EXPLOTA-TION OF RESULTS(maximum 1 page)

The following items must be described:

� Scientific and technical contributions expected from the project, potential application or transfer of the ex-pected results in the short, medium or large term, benefits derived from the increase of knowledge andtechnology.

� Diffusion plan and, if appropriate, exploitation plan of the results.

5.1 Scientific and Technical contributions

Publications: From 2000 (see 6.0.2), the group has published more than 120 papers in ISI or MathSciNetjournals, in the general subject of dynamical systems. This corresponds to the topic area 8.3 of theNational Program in Mathematics, although some applications appear published in journals of otherresearch areas. Moreover, 7 monographs have been published during this period. For the 2006-2009period, the group expects to publish about 130 papers in MathSciNet or ISI journals with a high impactfactor.Communications and Talks in Scientific Conferences: From 2000, the group has taken part in morethan 250 conferences (more than 150 of which are international, see 6.0.3), many of them plenary orinvited. For the period 2006-2009, it is expected to participate in about 230 conferences.Ph.D. Thesis: From 2001, 6 people of the group have defended their l Ph.D. thesis. It is expected thatabout 9 thesis will be finished in the period 2006-2009.5.2 Communication of the Results

Organization of Events: As it is reflected in 6.0.1, from the year 2000 the group has participated inthe organization of 17 conferences, symposia, workshops and courses, most of them international. It isexpected to continue in this line. In particular, during 2006 the group is involved in the organization ofCarles Simo Fest, No Lineal 2006/7, a symposium in IV Inter. Conf. Dynam. Systems Diff. Equations,DDays06 and in the Conference on Mathematical Neuroscience.Courses and Seminars: Besides the usual internal group meetings, we receive invitations of externalseminars and research courses that are expected to continue. As examples of some courses, we mention:El Escorial 2003, Instituto de Matematicas y Ciencias Afines de Peru 2004, Universidad Sergio Arboledade Bogota 2004, Instituto Nacional de Pesquisas Espaciais de Brasil 2004, Community of Ariane Cities2005. Moreover, our group also organizes periodically Winter and Summer Schools (see section 7).Popularization of the results to students and Mass Media: Regularly the members of the group givelectures to high-school and undergraduate students. Due to the impact of some of the results, the researchof the group has appeared in regular journals (El Paıs, La Vanguardia, El Punt, El Mundo and ABC)and other media. Also in popular science magazines (Gaceta de la RSME, Caltech’s Engineering andScience, Scienze,. . . ). Invited talks have been given in The Biennal Conference of the World Councilfor Gifted and Talented Children (2001), First Aurora Student Design Contest of ESA (2003), Board ofEuropean Students of Technology (2003). We expect to continue with this kind of activities which weconsider important to attract new students and as a way to advertise our group’s “brand”.Web pages: The documentation generated by the groups can be found in http://www.ma1.upc.eduand in the UB-UPC dynamical systems group website, http://www.maia.ub.es/dsg. We also gatherinformation and results (internal and external) on specific topics in the webs: http://www.ieec.fcr.es/astro04, http://www.dance-net.org/ or http://www.ieec.fcr.es/libpoint/inici.html.5.3 Technology transfer

Projects: The group collaborates regularly as a consultant with NASA-JPL (TPF missions of formationflight and orbit transfer in JIMO), with Deimos Space SL and Alcatel (more details in 6.1). In the project,reports from Deimos Space S.L. and JPL are attached.Training of Professionals: These collaborations are a consequence of the multidisciplinarity of the group.The combination of a broad spectrum of applied analytical and numerical techniques, jointly with awell-founded theoretical background, has made the group leader in the field of advanced technologieswhere complex studies and modelling are required. For the same reason, we receive a large number ofapplications from foreign students. The Ph.D. students in the group learn, during their training period,a broad range of techniques and methodology that make them very attractive to cutting-edge technologycompanies that request and hire them when their thesis finishes. More details can be found in Section 7.

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6.BACKGROUND OF THE GROUP(In the case of a coordinated project the topics 6. and 6.1. must be filled by each partner)(maximum 2 pages)

� Indicate the previous activities and achievements of the group in the field of the project:

– If the project is related to other previously granted, you must indicate the objectives and the results achievedin the previous project.

– If the project approaches a new research field, the background and previous contributions of the group inthis field must be indicated in order to justify the capacity of the group to carry out the project.

6.0.0 Attained goals and achieved results

The project we present is a continuation of the previously financed projects BFM2003-09504 Invariantobjects in dynamical systems, their connections, evolution with respect to parameters and applications(linked with the UPC) and BFM2003-07 521-C02-01 Recurrent dynamics and applications (linked withthe UB). The team of the present project have contributed with the following achievements to theobjectives of the former projects:

Invariant objects in dynamical systems In the last years, the group has been conspicuous in thestudy of KAM theory, with important results on the persistence of invariant tori in cases like thequasiperiodic Hopf bifurcation, in bifurcations related to resonances between normal frequencies andexternal frequencies in quasiperiodic perturbations of oscillators or the existence of secondary invarianttori (that should play an important role in the Arnold diffusion), and also near the splitting of invari-ant tori of twist maps close to integrable. Moreover, we have introduced KAM methods allowing thecomputation of invariant tori without the formalism of canonical transformations (that can be used asa numerical tool or to perform assisted computed proofs for the existence of invariant tori). The grouphas also made important contributions in the effective computation of invariant objects by means of thedesign and implementation of normal forms algorithms.

Integrability The extension of the main result of the Morales-Ramis theory to variational equations ofhigher order has been achieved in [176]. This result, that was conjectured in [45], allows to completelyclose the problem of integrability of the classic Henon-Heiles family, and it opens new perspectives in thestudy of integrability criteria.

The discrete Lagrangian formalism with discrete non-holonomic constraints has been applied to the casewhere the configuration space is a Lie group G, and the constraints are left invariant. As an application,integrable discretizations of the classical non-holonomic systems of Suslov and Chaplygin have beenconstructed. The discrete problems of Suslov and Chaplygin mantain almost all the main properties oftheir continuous analogs [102, 103]. A new method for the explicit construction of all the closed algebraicgeodesic on a tri-axial ellipsoid has also been developed [101].

Complex dynamics We have obtained results about the asymptotic behavior of the size of the Hermanrings of Arnold’s family of circle maps [97]. The numerical verification of these results requires theobtention of new numerical methods to compute efficiently the rotation number. These methods will bedeveloped in project [BV1].

Connections between invariant objects The group has advanced in the study of Arnold diffusionas an instability mechanism, and this has been partially described by means of the scattering map.Together with the diffusion and chaotic behavior, important results on the splitting of separatrices havebeen obtained, justifying its computation at first order from the Melnikov potential function, or also bymeans of resurgence techniques. Other results concern the persistence of biasymptotic orbits in ellipticbilliards.

Evolution with respect to parameters of invariant objects and their connections J. Puig hassolved the Ten Martini Problem concerning the spectrum of the Mathieu operator, even proving a strongversion of the result for sufficiently small or big potentials. He has also proved the regularity of the bound-aries of the resonance tongues that appear in the plane of parameters of the quasiperiodic Hill equationand he has analyzed the appearance of instability pockets of these tongues. For these investigations, hehas received the prize “Jose Luis Rubio de Francia” in 2005.

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Applications of the invariant objects and their connections The group has advanced in the de-sign of tools that allow to control the arrival and departure phases to periodic orbits and invariant tori.Families of planar connections for transfer orbits in the Earth-Moon and Earth-Sun system have beencomputed. Finally, the theoretical basis for trajectory generation algorithms with specific itineraries hasalso been obtained.

The detailed contributions are reflected in the references.

6.0.1 Background of the Group

During the last 10 years, the dynamical systems group at the “Universitat Politecnica de Catalunya(UPC)” (see http://www.ma1.upc.edu/recerca/pestanyarecerca esp.html#sistemes) has been col-laborating closely with the dynamical systems group at the “Universitat de Barcelona (UB)”, formingtogether the dynamical systems groups UB-UPC (http://www.maia.ub.es/dsg/), that is currently aworldwide leader group in the development of analytic and numerical methods for the study of dynamicalsystems.

The largest part of the team are members of the coordinated project BFM2003-09504 Invariantobjects in dynamical systems, their connections, evolution with respect to parameters and applications(those presently linked with the UPC), but we have to add five members of the project BFM2003-07 521-C02-01 Recurrent Dynamics and applications (also currently linked with the UPC), and two members ofthe DSG group at the UAB (http://www.gsd.uab.es/). Given the growth of the UPC team, we felt iswas convenient to divide the two teams in the current application.

The strong growth of the UPC team in the last years is basically due to researchers that have recentlyjoined the team: 1 ICREA researcher, 2 “Ramon y Cajal” researchers, 1 “Juan de la Cierva” researchersand 8 new graduate students with scholarship. Currently, the group has 18 doctors (Ph.D.) linked withthe UPC, 4 of which have partial dedication, and 8 graduate students linked with the UPC, all of themat full-time; 3 other researchers, one of them at part-time, belong to other universities.

We would also like to mention the high capacity of the group in the formation of new researchers:the number of graduate students (with or without scholarship) is 9, and 5 former graduate students havegraduated in the group in the last 5 years. This activity is developed in the Ph.D. program of AppliedMathematics, that owns a “quality mention” and it is coordinated by T. M-Seara.

The key in the quantitative and qualitative enlargement of the group is due to specific factors like:

• The quality and quantity of publications in international highly prestigious journals, as it can be seenin the reference list appended at the end of this section. Roughly, the group’s scientific output from2000 can be summarized in more than 120 papers in ISI or MathSciNet journals, 9 monograph booksand about 30 chapters of books. Most of the papers have appeared in high-level mathematical journals,like J. Nonlinear Sci., Comm. Math. Phys., Phys. D, Mem. Amer.Math. Soc., Nonlinearity, Chaos,J. Differ. Equations, Adv. Math., etc.

• The involvement in several editorial boards of scientific journals, like Collect. Math. (R. de la Llave),Discrete Contin. Dynam. Systems (A. Delshams), Experiment. Math. (R. de la Llave), J. Math. Phys.,(R. de la Llave), J. Nonlinear Sci. (A. Delshams), Math. Phys. Electron. J. (R. de la Llave), SIAM J.Math. Anal. (R. de la Llave), Book Ser. Contemp. Math. (R. de la Llave), Tut. Rev. DsWeb SIAM(R. de la Llave), Nonlinearity (R. de la Llave) y Electronic Journal of Mathematical and Physical Sciences(R. de la Llave).

• The involvement in scientific committees or scientific prizes, like in the RSME (A. Delshams, J.J. Morales),of activities of the DANCE net (A. Guillamon, T. M.-Seara), of the conference Neuromath06 (A. Guil-lamon), of the AMS Program committee Central Section (R. de la Llave), External visiting committee ofthe Univ. Carlos III (R. de la Llave), of the AMS Program committee Joint Meeting with RSME (R.de la Llave), of the conference V Jornadas de trabajo en mecanica celeste (M. Olle), of the conferenceLibration Point Orbits And Applications (J. Masdemont), of the advanced course Summer Workshop onAdvanced Topics in Astrodynamics (J. Masdemont).

• The large number of plenary and invited talks in interantional conferences: more than 250; of which morethan 150 in international conference (see also the appended curriculum vitae).

• The involvement in the organization of conferences, symposia, workshops and courses, national andinternational, like:

No Lineal 2000 (Almagro, May 2000, A. Delshams); 4th DSDE (Wilmington, May 2002, A. Delshams);No Lineal 2002 (Cuenca, June 2002, A. Delshams); LibPoint02 , (Girona, June 2002, G. Gomez and

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J. Masdemont); Jornadas de Introduccion a los Sistemas Dinamicos, (Barcelona, June 2002, 2003 and2004, T.M. Seara; June 2005, A. Guillamon); V. Lazutkin Conference (St.-Petersburg, Aug. 2002,A. Delshams); DMDE’02 (Valladolid, Sep. 2002, A. Delshams); COM & COM (Barcelona, May 2003,A. Delshams); AMS-RSME (Sevilla, June 2003, R. de la Llave and T.M. Seara). Summer School onNonlinear Phenomena in Computational Chemical Physics (Barcelona, June 2003, F. Gabern); XVIIICEDYA(Tarragona, Sep. 2003, C. Olive); No Lineal 2004 (Toledo, June 2004, A. Delshams); CRMTrimester On Control, Geometry And Engineering (Barcelona, Jan-Mar 2005, A. Delshams); JornadasCientıficas RSME: Matematicas y Analisis de Misiones, Telecomunicaciones y Matematicas (Barcelona,June 2005, A. Delshams); EMS-SCM Joint Mathematical Weekend (Barcelona, September 2005, T. M.-Seara); NSDS05: Non-autonomous & Stochastic Dynamical Systems(Sevilla, September 2005, Delshams);Carles Simo Fest (S’Agaro, May-June 2006, A. Delshams). No Lineal 2006 (Almagro, June 2006,A. Delshams); The Sixth International Conference on Dynamical Systems and Differential Equations,Symposium Hamiltonian Systems (Poitiers, June 2006, A. Delshams); Conference on Mathematical Neu-roscience (Andorra, September 2006, A. Guillamon); responsible of the neuroscience branch in the ProjectShaping New Directions in Mathematics for Science and Society (MATHFSS) of the program New andEmerging Science and Technology (NEST) of the European Commission (2005-07, A. Guillamon). Ob-serve that the last 5 activities will take place in the near future.

We would like to mention that A. Delshams has been the leader, jointly with L. Alseda, of the creation andcoordination of the DANCE scientific network, (http://www.dance-net.org) and that some members ofthe group have been involved in the organization and scientific committees of its activities: DDAYS 2003(Salou), DDAYS 2004 (Murcia), DDAYS 2006 (Sevilla), RTNS 2004 (Mallorca), RTNS 2005 (Castello),RTNS 2006 (Oviedo). Furthermore, the group co-organizes the following seminars (Seminar of the Dy-namical Systems Group UB-UPC, Aula de Sistemes Dinamics, NeuroMat , discussion meetings . . . ). Asit is easy seen, the groups is not only very active in scientific publications but also in the promotion andmanagement of scientific activities.

• Prizes: Jose Luıs Rubio de Francia RSME (J. Puig, 2005), Evarist Galois, SCM (J. Puig, 2003).

• The involvement and coordination of projects and networks of international cooperation. Putting togetherall types of projects and networks, the UPC group has been involved, during the last 5 years, in 38 projects(17 of them, directed by team members, and 12 international), up to a total amount of 1.213.825,25 euros.For a more detailed information, see section 6.1.

We have also obtained the mention “grupo de investigacion consolidado” by the Generalitat de Catalunyain all the announcements: 1996SGR-00105, 1998SGR-00041, 2000SGR-00027 (11), 2001SGR-00070 (12)and 2001SGR-00173 (2).

The thematic network DANCE (“Dinamics, Attractors and Nolineality: Chaos and Stability”), coordi-nated by A. Delshams jointly with L. Alseda, which currently forms a group of more than 100 people, hasobtained the following projects (in brackets, the number of participants in the UPC group are shown):BFM2002-12129-E (15), BFM2001-5237-E (14), 2002/XT/00094 (12), 2004/XT/00053 (11).

• The multiple collaborations with national and international groups (see section 6.0.5 on collaboratorgroups), that take place in long stays of the group members or in short visits of other groups researchers.In particular, we would like to mention the close relationship with the Univ. of Texas at Austin and theUniversity of Moscow, that has resulted the involvement of R. de la Llave and Y. Fedorov in the currentproject.

• The maintenance and upgrade, by some of the UPC group members, of the Beowulf cluster EIXAM (see,http://www-ma1.upc.es/eixam/). The steps taken in the lasts years have led to an ambitious updatingtask, that is currently taking place. The new machine will have approximately 25 computers, each oneof them with 2GB of RAM memory and a double processor Intel Xeon a 3.2GHz cache 2MB. This willraise the sustained present computational power to more than 250 Gflops, multiplying by more than 50the capacity of the older machine.

• Finally, the scientific leadership position in several research areas in dynamical systems:

Integrability Both the articles on nonintegrability, mainly due to J.J. Morales [169, 172, 175, 173],and those of Y. Fedorov [59, 60, 61, 62, 63, 98, 99, 100] on integrability, head this field. Besides, themonograph [45] by J.J. Morales is nowadays the standard reference on the applications of differentialGalois theory to the nonintegrability of Hamiltonian systems.

Invariant Objects and K.A.M. theory Many remarkable results have been obtained, both in K.A.M.(and Nekhoroshev) theory and on the existence of invariant manifolds [67, 72, 84, 91, 160, 181, 191].

25

This has been done, mainly, by R. de la Llave, and, also, A. Delshams, A. Guillamon, P. Gutierrez, T.Lazaro, M. Olle, J.R. Pacha, R. Ramırez, T.M. Seara and J. Villanueva. Moreover, R. de la Llave haspublished in [151] the present state-of-the-art in K.A.M. theory.

Conjugation R. de la Llave is a reputed expert in this field [156, 161]. J. Puig in [184] consideredone-dimensional spectral problems in quasi-periodic Schrodinger operators using the conjugation of thedynamical systems associated to their eigenvalue equation. This lead to the proof of an old conjectureknown as the “Ten Martini Problem”, open for more than forty years. This work has motivated a lotof activity in the area and has lead to the proof of several other open problems, see [185].

Poincare-Melnikov method A. Delshams, R. Ramırez and P. Gutierrez [66, 85, 19, 20, 83, 152, 153]have developed geometrical methods aimed at obtaining compact formulae for the splitting of separa-trices in Hamiltonian systems or symplectic maps.

Exponentially small separatric splitting Due to the close collaboration with the group the Univ. ofSt. Petersbourg, some of the most powerful methods in the field have been obtained by A. Delshams,P. Gutierrez, R. Ramırez and T.M. Seara [86, 87, 88, 89], to cite only the most recent ones.

Diffusion This is a very promising area, where methods developed within the group [92, 93, 94, 95, 108,109, 110, 111] by Delshams, R. de la Llave, P. Martın and T.M. Seara are increasingly being used byother researchers. An indicator of the international recognition on the results obtained in the group isthat the invited conference of R. de la Llave in the ICM2006 will be based on this subject.

Astrodynamics and Celestial mechanics The results by J. Masdemont, together with G. Gomez,A. Jorba y C. Simo [UB], being [127, 128, 131, 133] the most recent ones, are based on the applicationof geometrical methods (the configuration of invariant manifolds) for the analysis and design of spacemissions and are at the cutting-edge of current research. This is reflected in the collaboration withNASA-JPL in several missions. Part of the methodology developed by the group has been recentlyreviewed in [125, 126].These works, and more by F. Gabern, have been acknowledged as outstanding contributions to missiondesign in a recent article by J. E. Marsden et al [41].We also highlight [82] as a contribution to the study of central configurations; [166] in the context ofperiodic and quasiperiodic motions in the restricted three body problem and the topic of the quasiperi-odic Hamiltonian Hopf bifurcation in this problem (see [150, 180]), considered by M. Olle, J.R. Pachay J. Villanueva.

Return and Period Maps In recent years, A. Guillamon, joinlty with researchers from other univer-sities, has taken part significant contributions towards the comprehension of temporal phenomena indifferential equations in the plane (see [112, 113, 114, 123]). The most recent results are aimed atdescribing with the same objects both the time and the stability of orbits (see [28]).

26

6.0.2 References of the group since 2004

At the end of each reference is shown, if applicable, the impact factor (IF) and the classification ofits journal inside its ISI category, as well as its MathSciNet reference.

[59] S. Abenda and Yu. Fedorov, On the weak Kowalevski-Painleve property for hyperelliptically separable systems,Acta Appl. Math., 60 (2000), 137–178. MR 2001h:37123 25

[60] S. Abenda and Yu. Fedorov, Complex angle variables for constrained integrable Hamiltonian systems, J. NonlinearMath. Phys. 8 (2001), 1–4. [II: 0.585; Clas: 26/34]; MR 2001m:37119 25

[61] M.S. Alber, R. Camassa, Yu. Fedorov, D.D. Holm and J.E. Marsden, The complex geometry of weak piecewisesmooth solutions of integrable nonlinear PDE’s of shallow water and Dym type, Comm. Math. Phys. 221 (2001),197–227. [II: 1.741; Clas: 7/34]; MR 2002f:37110 25

[62] M.S. Alber and Yu. Fedorov, Wave solutions of evolution equations and Hamiltonian flows on nonlinear subvarietiesof generalized Jacobians, J. Phys. A, 33 2000, 8409–8425. MR 2002f:37123 25

[63] M.S. Alber and Yu. Fedorov, Algebraic geometrical solutions for certain evolution equations and Hamiltonianflows on nonlinear subvarieties of generalized Jacobians, Inverse Problems 17 (2001), 1017–1042. [II: 1344; Clas:10/162]; MR 2002i:35158 25

[64] A. Apte, R. de la Llave and N.P. Petrov, Regularity of critical invariant circles of the standard nontwist map,Nonlinearity 18 (2005), 1173–1187. [II: 0.962; Clas: 31/162]; MR2134890

[65] C.A. Beichman, G. Gomez, M.W. Lo, J.J. Masdemont and L. Romans, Searching for Life with the TerrestrialPlanet Finder: Lagrange Point Options for a Formation Flying Interferomete, Advances in Space Research 34(2004), 637–644. [II: 0.548; Clas: 36/45]

[66] S. Bolotin, A. Delshams and R. Ramırez-Ros, Persistence of homoclinic orbits for billiards and twist maps,Nonlinearity 17 (2004), 1153–1177. [II: 0.962; Clas: 31/162]; MR 2005d:37126 12, 26

[67] H.W. Broer, H. Hanßmann, A. Jorba, J. Villanueva and F. Wagener, Normal-internal resonances in quasi-periodically forced oscillators: a conservative approach, Nonlinearity 16 (2003), 1751–1791. [II: 0.962; Clas:31/162]; MR 2004i:37111 5, 25

[68] H.W. Broer, J. Puig and C. Simo, Resonance tongues and instability pockets in the quasi-periodic Hill-Schrodingerequation. Comm. Math. Phys., 241 (2003), 467–503. [II: 1.741; Clas: 7/34]; MR 2004j:37028 17

[69] X. Cabre, E. Fontich and R. de la Llave, The parameterization method for invariant manifolds I: manifoldsassociated to non-resonant subspaces, Indiana Univ. Math. J. 52 (2003), 283–328. [II: 0.784; Clas: 31/181]; MR2004h:37030

[70] X. Cabre, E. Fontich and R. de la Llave, The parameterization method for invariant manifolds II: regularity withrespect to parameters, Indiana Univ. Math. J. 52 (2003), 329–360. [II: 0.784; Clas: 31/181]; MR 2004h:37031

[71] X. Cabre, E. Fontich and R. de la Llave, The parameterization method for invariant manifolds III: overview andapplications, J. Differential Equations 218(2) (2005), 444-515. [II: 0.877; Clas: 24/181]; MR2177465

[72] L.A. Caffarelli and R. de la Llave, Planelike minimizers in periodic media, Comm. Pure Appl. Math. 54 (2001),1403–1441. [II: 1.694; Clas: 5/162]; MR 2002j:49003 25

[73] L.A. Caffarelli and R. de la Llave, Interfaces of ground states in Ising models with periodic coefficients,J. Stat. Phys. 118 (2005), 687–719. [II: 1.747; Clas: 6/34]; MR2123651

[74] F. Calogero, D. Gomez-Ullate, P. Santini and M. Sommacal, The transition from ordered to disorded motions,explained as travels on Riemann surfaces, J. Phys. A 38 (2005), 8873–8896. [II: 1.504; Clas: 11/34]

[75] E. Canalias, J. Cobos and J.J. Masdemont, Impulsive transfers between Lissajous libration point orbits, J. As-tronautical Sci. 51 (2003), 361–390. [II: 0.364; Clas: 14/25]; M 2006b:70035

[76] E. Canalias and J.J. Masdemont, Homoclinic and heteroclinic connections between planar Lyapounov orbits inthe restricted three-body problem, Discrete Contin. Dyn. Syst. 14 (2006), 261–279. [II: 0.994; Clas: 14/181];MR2163533

[77] P.S. Casas and A. Jorba, Unstable manifold computations for the two-dimensional plane Poiseuille flow, Theoret-ical Comput. Fluid Dynamics 18(2-4) (2004), 285–299.

[78] P.S. Casas and R. Quintanilla, Exponential decay in one-dimensional porous-thermo-elasticity, Mech. Res. Comm.,32 (2005), 652–658. [II: 0.957; Clas: 28/107]; MR2158183

[79] P.S. Casas and R. Quintanilla, Exponential stability in thermoelasticity with microtemperatures, Int. J. Engi-neering Sci., 43 (2005), 33–47. [II: 1.065; Clas: 10/61]; MR2112810

[80] C. Christopher, J. Llibre, Ch. Pantazi and X. Zhang, Darboux integrability and invariant algebraic curves forplanar polynomial systems, J. Phys. A 35 (2002), 2457–2476. [II: 1.504; Clas: 11/34]; MR 2003c:34037

[81] D. Cordoba, Ch. Fefferman and R. de la Llave, On squirt singularities in hydrodynamics, SIAM J. Math. Anal.36 (2004), 204–213. [II: 0.966; Clas: 29/162]; MR 2005i:76032

[82] J.M. Cors, J. Llibre and M. Olle, Central configurations of the planar coorbital satellite problem, CelestialMech. Dyn. Astronom. 89 (2004), 319–342. [II: 0.720; Clas: 33/52]; MR 2005h:70012 26

[83] A. Delshams, Yu. Fedorov and R. Ramırez Ros, Homoclinic billiard orbits inside symmetrically perturbed ellip-soids, Nonlinearity 14 (2001), 1141–1195. [II: 0.962; Clas: 31/162]; MR 2002h:37120 12, 26

[84] A. Delshams, A. Guillamon and J.T. Lazaro, A pseudo-normal form for planar vector fields, Qual. TheoryDyn. Syst. 3(1) (2002), 51–82. MR2109559 5, 25

[85] A. Delshams and P. Gutierrez, Splitting potential and Poincare–Melnikov method for whiskered tori in Hamilto-nian systems, J. Nonlinear Sci. 10(4) (2000), 433–476. [II: 1.850; Clas: 4/162]; MR 2001d:37094 4, 26

27

[86] A. Delshams and P. Gutierrez, Exponentially small splitting of separatrices for whiskered tori in Hamiltoniansystems, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 300 (2003), 87–121. MR 2004j:3711911, 26

[87] A. Delshams and P. Gutierrez, Exponentially small splitting for whiskered tori in Hamiltonian systems: contin-uation of transverse homoclinic orbits, Discrete Contin. Dyn. Syst. 11 (2004), 757–783. [II: 0.994; Clas: 14/181];MR 2005j:37101 11, 26

[88] A. Delshams and P. Gutierrez, Exponentially small splitting of separatrices for whiskered tori in Hamiltoniansystems, J. Math. Sci. 128 (2005), 2726–2746. MR 2004j:37119 4, 26

[89] A. Delshams, P. Gutierrez and T.M. Seara, Exponentially small splitting for whiskered tori in Hamiltoniansystems: flow-box coordinates and upper bounds, Discrete Contin. Dyn. Syst. 11 (2004), 785–826. [II: 0.994;Clas: 14/181]; MR2112704 11, 26

[90] A. Delshams and J.T. Lazaro, Pseudo-normal form near saddle-center or saddle-focus equilibria, J. DifferentialEquations, 208 (2005), 312–343. [II: 0.877; Clas: 24/181]; MR2109559 5

[91] A. Delshams and R. de la Llave, KAM theory and a partial justification of Greene’s criterion for non-twist maps,SIAM J. Math. Anal., 31(6) (2000), 1235–1269. [II: 0.966; Clas: 29/162]; MR 2001j:37079 25

[92] A. Delshams, R. de la Llave and T.M. Seara, A geometric approach to the existence of orbits with unboundedenergy in generic periodic perturbations by a potential of generic geodesic flows of T2, Comm. Math. Phys. 209(2000), 353–392. [II: 1.741; Clas: 7/34]; MR 2001a:37086 4, 11, 26

[93] A. Delshams, R. de la Llave and T.M. Seara, A geometric mechanism for diffusion in Hamiltonian systemsovercoming the large gap problem: Announcement of results, ERA Amer. Math. Soc. 9 (2003), 125–134. MR2004j:37118 26

[94] A. Delshams, R. de la Llave and T.M. Seara, Orbits of unbounded energy in quasi-periodic perturbations ofgeodesic flows, accepted in Adv. Math. (2005). [II: 1.067; Clas: 13/181] 4, 26

[95] A. Delshams, R. de la Llave and T.M. Seara, A geometric mechanism for diffusion in Hamiltonian systemsovercoming the large gap problem: heuristics and rigorous verification on a model, Memoirs Amer. Math. Soc.844 (2006), 1–161. [II: 1.193; Clas: 10/181] 4, 11, 26

[96] M.V. Deryabin and Yu. Fedorov, On reductions for a group of geodesic flows with (left-) right-invariant metricand their symmetry fields, Dokl. Akad. Nauk 391 (2003), 439–442. MR 2004i:37120

[97] N. Fagella, T.M. Seara y J. Villanueva, Asymptotic size of Herman rings of the complex standard family by quan-titative quasiconformal surgery, Ergodic Theory Dynam. Systems 24 (2004), 735–766. [II: 0.484; Clas: 101/162];MR 2005c:37083 23

[98] Yu. Fedorov, Integrable systems, Poisson pencils, and hyperelliptic Lax pairs, Regul. Chaotic Dyn., 5, 2000,171–180. MR 2001e:37074 25

[99] Yu. Fedorov, An ellipsoidal billiard with quadratic potential, Funktsional. Anal. i Prilozhen. 35 (2001), 48–59.MR 2002h:37108 25

[100] Yu. Fedorov, Backlund transformations on coadjoint orbits of the loop algebra gl(r), J. Nonlinear Math. Phys. 9(2002), 29–46. [II: 0.585; Clas: 26/34]; MR 2003j:37086 25

[101] Yu. Fedorov, Algebraic closed geodesics on a triaxial ellipsoid, Regul. Chaotic Dyn. 10 (2005), 463–485. 23[102] Yu. Fedorov and B. Jovanovic, Nonholonomic LR systems as generalized Chaplygin systems with an invariant

measure and flows on homogeneous spaces J. Nonlinear Sci. 14 (2004), 341–381. [II: 1.850; Clas: 4/162]; MR2005d:37136 23

[103] Yu. Fedorov and D.V. Zenkov, Discrete nonholonomic LL systems on Lie groups, Nonlinearity 18 (2005), 2211–2241. [II: 0.962; Clas: 31/162]; MR2164739 23

[104] F. Finkel, D. Gomez-Ullate, A. Gonzalez-Lopez, M.A. Rodrıguez and R. Zhdanov, AN -type Dunkl operatorsand new spin Calogero-Sutherland models Comm. Math. Phys. 221 (2001), 477–497. [II: 1.741; Clas: 7/34]; MR2003b:81075

[105] F. Finkel, D. Gomez-Ullate, A. Gonzalez-Lopez, M.A. Rodrıguez and R. Zhdanov, New spin Calogero-Sutherlandmodels related to BN -type Dunkl operators, Nuclear Phys. B 613 (2001), 472–496. [II: 5.819; Clas: 4/21]; MR2002h:81101

[106] F. Finkel, D. Gomez-Ullate, A. Gonzalez-Lopez, M.A. Rodrıguez and R. Zhdanov, On the Sutherland spin modelof BN type and its associated spin chain, Comm. Math. Phys. 233 (2003), 191–209. [II: 1.741; Clas: 7/34]; MR2005c:82016

[107] E. Fontich, R. de la Llave and P. Martın, Invariant pre-foliations for non-resonant non-uniformly hyperbolicsystems, Trans. Amer. Math. Soc., 358 (2006), 1317–1345. [II: 0.839; Clas: 27/181]

[108] E. Fontich and P. Martın, Differentiable invariant manifolds for partially hiperbolic tori and a lambda lemma,Nonlinearity, 13 (2000), 1561–1593. [II: 0.962; Clas: 31/162]; MR 2002j:37086 26

[109] E. Fontich and P. Martın, Arnold diffusion in perturbations of analytic exact symplectic maps, Nonlinear Analysis,TMA, 42 (2000), 1397–1412. [II: 0.459; Clas: 77/181]; MR 2001g:37088 26

[110] E. Fontich and P. Martın, Arnold diffusion in perturbations of analytic integrable Hamiltonian systems, DiscreteContin. Dyn. Syst. 7 (2001), 61–84. [II: 0.994; Clas: 14/181]; MR 2001k:37096 (Citado por 14) 26

[111] E. Fontich and P. Martın, Hamiltonian systems with orbits covering densely submanifolds of small codimension,Nonlinear Anal. 52 2003, 315–327. [II: 0.459; Clas: 77/181]; MR 2003h:37096 26

[112] E. Freire, A. Gasull and A. Guillamon, Period function for perturbed isochronous centres Qual. Theory Dyn. Syst.3 (2002), 275–284. MR 2004b:34112 26

28

[113] E. Freire, A. Gasull and A. Guillamon, A characterization of isochronous centres in terms of symmetries,Rev. Mat. Iberoamericana 20 (2004), 205–222. [II: 0.565; Clas: 54/181]; MR 2005c:34067 26

[114] E. Freire, A. Gasull and A. Guillamon, First derivative of the period function with applications, J. DifferentialEquations 204 (2004), 139–162. [II: 0.877; Clas: 24/181]; MR 2005f:37049 26

[115] F. Gabern and A. Jorba, A restricted four-body model for the dynamics near the Lagrangian points of the Sun-Jupiter system, Discrete Contin. Dyn. Syst. Ser. B 1 (2001), 143–182. [II: 1.310; Clas: 12/162]; MR 2002g:70020

[116] F. Gabern and A. Jorba, Generalizing the Restricted Three-Body Problem. The Bianular and Tricircular CoherentProblems, Astronomy & Astrophysics 420 (2004), 751–762. [II: 3.694; Clas: 10/45]; Zbl 1072.85004

[117] F. Gabern and A. Jorba, Effective computation of the dynamics around a two-dimensional torus of a Hamiltoniansystem, J. Nonlinear Sci. 15 (2005), 159–182. [II: 1.850; Clas: 4/162]; MR2151929

[118] F. Gabern, A. Jorba and U. Locatelli, On the construction of the Kolmogorov normal form for the Trojan asteroids,Nonlinearity textbf18 (2005), 1705–1734. [II: 0.962; Clas: 31/162]; MR 2005m:70057

[119] F. Gabern, A. Jorba and P. Robutel, On the accuracy of Restricted Three-Body Models for the Trojan motion,Discrete Contin. Dyn. Syst. 11 (2004), 843–854. [II: 0.994; Clas: 14/181]; MR 2005h:70013

[120] F. Gabern, W.S. Koon and J.E. Marsden, Parking a spacecraft near an asteroid pair, accepted in J. Guid. ControlDyn. (2005). [II: 0.852; Clas: 5/25]

[121] F. Gabern, W.S. Koon, J.E. Marsden and S.D. Ross, Theory and computation of non-RRKM lifetime distributionsand rates in chemical systems with three or more degrees of freedom, Phys. D 211 (2005), 391–406. [II: 1.666;Clas: 6/162]

[122] A. Gasull, A. Guillamon and V. Manosa, Phase portrait of Hamiltonian systems with homogeneous nonlinear-ities, Nonlinear Analysis: Theory, Methods & Applications, 42 (2000), 679–707. [II: 0.459; Clas: 77/181]; MR2001e:34051

[123] A. Gasull, A. Guillamon and J. Villadelprat, The period function for second-order quadratic ODEs is monotone,Qual. Theory Dyn. Syst. 4 (2003), 329–352. MR 2005k:34115 26

[124] M. Gidea and R. de la Llave, Topological methods in the instability problem of Hamiltonian systems, DiscreteContin. Dyn. Syst. 14 (2006), 295–328. [II: 0.994; Clas: 14/181]; MR2163534

[125] G. Gomez, A. Jorba, J.J. Masdemont and C. Simo, Dynamics and Mission Design Near Libration Points - Volume3. Advanced Methods for Collinear Points, World Sci. Pub., Monograph Ser. Math. 4, Singapore, xiv+187 pp.,ISBN 981–02–4211-5, 2001. MR 2003c:70041c 5, 26

[126] G. Gomez, A. Jorba, J.J. Masdemont and C. Simo, Dynamics and Mission Design Near Libration Points - Volume4. Advanced Methods for Triangular Points, World Sci. Pub., Monograph Ser. Math. 4, Singapore, x+262 pp.,ISBN 981–02–4210-7, 2001. MR 2003c:70041d 5, 26

[127] G. Gomez, W.S. Koon, M.W. Lo, J.E. Marsden, J.J. Masdemont and S.D. Ross, Invariant manifolds, the spatialthree-body problem and space mission design, Adv. Astronautical Sci. 109 (2002), 3–22. 5, 26

[128] G. Gomez, W.S. Koon, M.W. Lo, J.E. Marsden, J.J. Masdemont and S.D. Ross, Connecting orbits and invari-ant manifolds in the spatial restricted three-body problem, Nonlinearity 17 (2004), 1571–1606. [II: 0.962; Clas:31/162]; MR 2005k:70026 5, 26

[129] G. Gomez, M.W. Lo and J.J. Masdemont (eds.), Libration Point Orbits and Applications, World Scientific, ISBN981-238-363-8, 2003. 5

[130] G. Gomez, M. Marcote and J.J. Masdemont, Trajectory correction manoeuvres in the transfer to libration pointorbits, Acta Astronautica 56 (2005), 652-669. [II: 0.240; Clas: 17/25]

[131] G. Gomez and J. Masdemont, Libration Point Orbits: The State of the Art from the Dynamical Systems Approach,in Advances in Space Dynamics, Ed. A. Prado. ISBN 85–901487–1–8, 1–49, 2000. 5, 26

[132] G. Gomez and J. Masdemont, Some Zero Cost Transfers Between Libration Point Orbits, Advances in the Astro-nautical Sciences 105 (2000), 1199–1219.

[133] G. Gomez, J. Masdemont and J.M. Mondelo, Solar system models with a selected set of frequencies, Astronomy& Astrophysics 390 (2002), 733–749. [II: 3.694; Clas: 10/45] 26

[134] D. Gomez-Ullate, A. Gonzalez-Lopez and M.A. Rodrıguez, New algebraic many-body problems Journal of Physics,33 (2000), 7305-7335. MR 2001k:81100 6

[135] D. Gomez-Ullate, A. Gonzalez-Lopez and M.A. Rodrıguez, Exact solutions of a new elliptic Calogero-Sutherlandmodel, Phys. Lett. B 511 (2001), 112–118. [II: 4.619; Clas: 7/67]; MR 2002g:81051

[136] D. Gomez-Ullate, A. Gonzalez-Lopez and M.A. Rodrıguez, Quasi-exactly solvable generalizations of Calogero-Sutherland models, Teoret. Mat. Fiz. 127 (2001), 367–378. [II: 0.651; Clas: 24/34]; MR 2002g:81198

[137] D. Gomez-Ullate, N. Kamran and R. Milson, Supersymmetry and algebraic Darboux transformations, J. Phys. A37 (2004), 10065–10078. [II: 1.504; Clas: 11/34]; MR2100323

[138] D. Gomez-Ullate, N. Kamran and R. Milson, The Darboux transformation and algebraic deformations of shape-invariant potentials, J. Phys. A 37 (2004), 10079–10804. [II: 1.504; Clas: 11/34]; MR 2005f:81282

[139] D. Gomez-Ullate, N. Kamran and R. Milson, Quasi-exact solvability and the direct approach to invariant sub-spaces, J. Phys. A 38 (2005), 2005–2019. [II: 1.504; Clas: 11/34]; MR2124377

[140] D. Gomez-Ullate and M. Sommacal, Periods of the goldfish many-body problem, J. Nonlinear Math. Phys. 12(2005), 351–362. [II: 0.585; Clas: 26/34]; MR2117192

[141] O. Gonzalez and R. de la Llave, Existence of ideal knots, J. Knot Theory Ramifications 12 (2003), 123–133. [II:0.308; Clas: 128/181]; MR 2003j:57010

[142] A. Guillamon, An introduction to the mathematics of neural activity, Butlletı de la Societat Catalana de

29

Matematiques 19 (2004), 25–45.[143] A. Haro and R. de la Llave, New mechanisms for lack of equipartition of energy, Phys. Rev. Lett., 85 (2000),

1859–1862.[144] A. Haro and R. de la Llave, Las matematicas de la mecanica estadıstica y de la teorıa del caos Rev. Esp. de Fısica

14 (2000), 17–22.[145] A. Haro and R. de la Llave, A parameterization method for the computation of invariant tori and their whiskers

in quasi-periodic maps: rigorous results, accepted in J. Differential Equations (2005). [II: 0.877; Clas: 24/181][146] A. Haro and R. de la Llave, Manifolds at the verge of a hyperbolicity breakdown, accepted in Chaos (2005). [II:

1.942; Clas: 3/162][147] A.P. Itin, R. de la Llave, A.I. Neishtadt and A.A. Vasiliev, Transport in a slowly perturbed convective cell flow,

Chaos 12 (2002), 1043–1053. [II: 1.942; Clas: 3/162]; MR 2003m:76072[148] M. Jiang and R. de la Llave, Smooth dependence of thermodynamic limits of SRB measures, Comm. Math. Phys.

211 (2000), 303–333. [II: 1.741; Clas: 7/34]; MR 2001g:37038[149] M. Jiang and R. de la Llave, Linear Response Function for coupled hyperbolic attractors, Comm. Math. Phys.

261 (2006), 379–404. [II: 1.741; Clas: 7/34];[150] A. Jorba and M. Olle, Invariant curves near Hamiltonian-Hopf bifurcations of four-dimensional symplectic maps,

Nonlinearity 17 (2004), 691–710. [II: 0.962; Clas: 31/162]; MR 2004m:37098 26[151] A. Katok, R. de la Llave and Y. Pesin (eds.), Smooth ergodic theory and its applications, Proceedings of Symposia

in Pure Mathematics 69, American Mathematical Society (Providence, RI), x+881 pp., 2001. 4, 26[152] O. Koltsova, L. Lerman, A. Delshams and P. Gutierrez, Homoclinic orbits to invariant tori near a homoclinic

orbit to center–center–saddle equilibrium, Phys. D 201 (2005), 268–290. [II: 1.666; Clas: 6/162]; MR2123447 11,26

[153] O. Koltsova, L. Lerman, A. Delshams and P. Gutierrez, Homoclinic trajectories towards invariant tori of a nearly-integrable Hamiltonian system (in russian), accepted in Dokl. Akad. Nauk (2005). 26

[154] V. Kozlov and Yu. Fedorov, Integrable systems on a sphere with potentials of elastic interaction, Math. Notes,56 (2005), 381–386. 4

[155] R. de la Llave, La ciencia del caos, in Las matematicas del siglo XX, num. 43-44, 473–476, Nivola, Madrid, 2000.[156] R. de la Llave, Remarks on Sobolev regularity in Anosov systems, Ergodic Theory Dynam. Systems 21 (2001),

1139–1180. [II: 0.484; Clas: 101/162]; MR 2002e:37040 26[157] R. de la Llave, Rigidity of higher-dimensional conformal Anosov systems, Ergodic Theory Dynam. Systems 22

(2002), 1845–1870. [II: 0.484; Clas: 101/162]; MR 2003h:37038[158] R. de la Llave, Invariant manifolds associated to invariant subspaces without invariant complements: a graph

transform approach Math. Phys. Electron. J. 9 (2003), 35 pp. (published electronically). MR 2005c:37045[159] R. de la Llave, Further rigidity properties of conformal Anosov systems, Ergodic Theory Dynam. Systems 24

(2004), 1425–1441. [II: 0.484; Clas: 101/162]; MR2104591[160] R. de la Llave, A. Gonzalez, A. Jorba and J. Villanueva, KAM theory without action-angle variables, Nonlinearity

18 (2005), 855–895. [II: 0.962; Clas: 31/162]; MR2122688 25[161] R. de la Llave and R. Obaya, Decomposition theorems for groups of diffeomorphisms on the sphere, Trans. AMS

352 (2000), 1005–1020. [II: 0.839; Clas: 27/181]; MR 2000j:58012 26[162] R. de la Llave and P. Panayotaros, Gravity waves on the surface of the sphere, in Mechanics from theory to

computation 85–100, Springer Verlag (2000). MR1766359[163] R. de la Llave and N.P. Petrov, Regularity of conjugacies between critical circle maps: an experimental study,

Experiment. Math. 11 (2002), 219–241. [II: 0.356; Clas: 116/181]; MR 2004g:37051[164] R. de la Llave and V. Sadovskaya, On the regularity of integrable conformal structures invariant under Anosov

systems, Discrete Contin. Dyn. Syst. 12 (2005), 377–385. [II: 0.994; Clas: 14/181] MR2119245[165] R. de la Llave and C.E. Wayne, Whiskered and low dimensional tori in nearly integrable Hamiltonian systems,

Math. Phys. Electron. J. 10 (2004), 45 pp. (electronico). MR2111299[166] J. Llibre and M. Olle, The motion of Saturn coorbital satellites in the restricted three-body problem, Astronomy

& Astrophysics 378 (2001), 1087–1099. [II: 3.694; Clas: 10/45]; ZM 1049.70009 26[167] J. Llibre and Ch. Pantazi, Polynomial differential systems having a given Darbouxian first integral, Bull. Sci. Math.

128 (2004), 775–788. [II: 0.385; Clas: 125/162]; MR 2005m:34070[168] J. Llibre and Ch. Pantazi, Counterexample to a conjecture on the algebraic limit cycles of polynomial vector

fields, J. Geom. Dedicata 110 (2005), 213–219. MR2136027[169] J.J. Morales-Ruiz, Kovalevskaya, Liapounov, Painleve, Ziglin and the differential Galois theory, Regul. Chaotic

Dyn., 5, 2000, 251–272. MR 2001i:37087 25[170] J.J. Morales-Ruiz, Meromorphic nonintegrability of Hamiltonian systems, Rep. Math. Phys., 48 (2001), 183–194.

[II: 0.652; Clas: 25/34]; MR 2002h:37105[171] J.J. Morales-Ruiz, A note on a connection between the Poincare-Arnold-Melnikov integral and the Picard-Vessiot

theory, Banach Center Publ. 58 (2002), 165–175. MR 2004c:37123[172] J.J. Morales-Ruiz and J.M. Peris, On the dynamical meaning of the Picard-Vessiot theory, Regul. Chaotic Dyn.

6 (2001), 277–290. MR 2002k:12018 25[173] J.J. Morales-Ruiz and J.-P. Ramis, Galoisian obstructions to integrability of Hamiltonian systems I, Methods

Appl. Anal. 8 (2001), 33–95. MR 2002m:37077 25[174] J.J. Morales-Ruiz and J.-P. Ramis, Galoisian obstructions to integrability of Hamiltonian systems II, Methods

30

Appl. Anal. 8 (2001), 97–111. MR 2002m:37077[175] J.J. Morales-Ruiz and J.-P. Ramis, A note on the non-integrability of some Hamiltonian systems with a homoge-

neous potential, Methods Appl. Anal. 8 (2001), 113–120. MR 2002m:37078 4, 25[176] J.J. Morales-Ruiz, J.-P. Ramis and C. Simo, Integrability of Hamiltonian Systems and Differential Galois Groups

of Higher Variational Equations, accepted in Ann. Sci. Ecole Norm. Sup. (4) (2006). 23[177] J.J. Morales-Ruiz, C. Simo and S. Simon, Algebraic proof of the non-integrability of Hill’s Problem, Ergodic

Theory Dynam. Systems 25 (2005), 1237–1256. [II: 0.484; Clas: 101/162]; MR2158404 4[178] C. Olive, D. Sauzin and T.M. Seara, Resurgence in a Hamilton-Jacobi Equation, Annales de l’Institut Fourier 53

(2003), 1185–1235. [II: 0.480; Clas: 72/181]; MR 2005b:37109 4[179] C. Olive, D. Sauzin and T.M. Seara, Two examples of resurgence, Contemporary Mathematics 373 (2005), 355–

371. MR 2005k:34343 4[180] M. Olle, J. R. Pacha and J. Villanueva, Motion close to the Hopf bifurcation of the vertical family of periodic

orbits of L4, Celestial Mech. Dynam. Astronom. 90 (2004), 89–109. [II: 0.720; Clas: 33/52]; MR 2005i:70012 13,26

[181] M. Olle, J.R. Pacha and J. Villanueva, Quantitative estimates on the normal form around a non-semi-simple 1:-1resonant periodic orbit, Nonlinearity 18 (2005), 1141–1172. [II: 0.962; Clas: 31/162]; MR2134889 13, 25

[182] M. Olle, J.R. Pacha and J. Villanueva, Dynamics close to a non semi-simple 1:-1 resonant periodic orbit, DiscreteContin. Dyn. Syst. Ser. B 5 (2005), 799–816. [II: 1.310; Clas: 12/162]; MR2151733 13

[183] N.P. Petrov, R. de la Llave and J.A. Vano, Torus maps and the problem of a one-dimensional optical resonatorwith a quasiperiodically moving wall, Phys. D 180 (2003), 140–184. [II: 1.666; Clas: 6/162]; MR 2004b:37122

[184] J. Puig, Cantor spectrum for the Almost Mathieu operator, Comm. Math. Phys. 244 (2004), 297–309. [II: 1.741;Clas: 7/34]; MR 2004k:11129 6, 14, 26

[185] J. Puig, A nonperturbative Eliasson’s reducibility theorem, Nonlinearity 19 (2006), 355–376. [II: 0.962; Clas:31/162]; 26

[186] J. Puig and C. Simo, Analytic families of reducible linear quasi-periodic equations, accepted in Ergodic TheoryDynam. Systems (2005). [II: 0.484; Clas: 101/162]

[187] R. Ramırez-Ros, Exponentially small separatrix splittings and almost invisible homoclinic bifurcations in somebilliard tables, Phys. D 210 (2005), 149–179. [II: 1.666; Clas: 6/162] MR2170615 12

[188] R. Ramırez-Ros, Break-up of resonant invariant curves in billiards and dual billiards associated to perturbedcircular tables, accepted in Phys. D (2006). [II: 1.666; Clas: 6/162] 14

[189] P. Robutel, F. Gabern and A. Jorba, The observed Trojans and the global dynamics around the Lagrangianpoints of the Sun-Jupiter system, Celestial Mech. Dynam. Astronom. 92 (2005), 53–69. [II: 0.720; Clas: 33/52];MR2177756

[190] D. Sauzin and T.M. Seara, Resumacio de Borel i teoria de la ressurgencia, Butlletı de la Societat Catalana deMatematiques 18 (2003), 131–153. MR 2005c:34179 4

[191] T.M. Seara and J. Villanueva, Asymptotic Behaviour of the Domain of Analyticity of Invariant Curves of theStandard Map, Nonlinearity, 13 (2000), 1699–1744. [II: 0.962; Clas: 31/162]; MR 2003a:37085 25

31

6.0.3 Conferences, stays and visits of the group members during the last 5 years

Conferences where a member of the group has given a talk or communication:

YEAR 2000

1. G. Gomez, J.J. Masdemont. “Some Zero Cost Transfers between Libration Point Orbits” (Talk). AAS/AIAA Space Flight Mechanics Meeting, Clearwater, USA, 23–26/ene 2000.

2. J.J. Masdemont. “Connecting Libration Point Orbits” (Invited Talk). LTool Developing Team Meeting,Jet Propulsion Laboratory NASA, Pasadena, CA, USA, 21 febrero 2000.

3. R. de la Llave. “Non-resonant invariant manifolds” (Talk). AMS sectional meeting, Notre Dame, 2000.4. T.M. Seara, J. Villanueva. “Asymptotic behaviour of the Domain of Analyticity of Invariant Curves of

the Standard map” (Talk). 953 AMS meeting, Notre Dame University, Indiana, USA, 8–9 Abr/2000.5. Yu. Fedorov. “Generalized Steklov systems and pencils of quadrics” (Invited Talk). Kowalevskaya

Workshop on Mathematical Methods in Regular Dynamics, Leeds, Reino Unido, abr 2000.6. Yu. Fedorov. “Integrable discrete systems as limits of continuous ones” (Invited Talk). Symposium on

PDE and special problems of ODE devoted to 150th anniversary of S. Kovalevskaya, Euler InternationalMathematical Institut and Mathematical Steklov Institute, St-Petersburgo, Rusia, may 2000.

7. J.J. Masdemont. “State of the Art in Libration Point Orbits” (Invited Talk). Workshop on Forma-tion Flying Near Libration Points. Interferometry, Formation Flying, and the Terrestrial Planet Finder(TPF), Jet Propulsion Laboratory NASA, Pasadena, CA, USA, 31 May –1 Jun 2000.

8. M.A. Andreu, J.J. Masdemont. “Reduccion a la Variedad Central alrededor de L2 del Problema Cuasi-bicircular” (Talk). No lineal 2000, Almagro, 31/may–3/jun 2000.

9. A. Guillamon, E. Freire, A. Gasull. “Condiciones de monotonıa de la funcion de perıodo” (Comunicacionoral). No Lineal 2000, Almagro, Mayo 31-Junio 3, 2000.

10. P. Gutierrez, A. Delshams. “Potencial de Melnikov y orbitas homoclınicas transversales en sistemashamiltonianos” (Talk). Nolineal 2000, Almagro, 31/may–3/jun 2000.

11. J.T. Lazaro, A. Delshams. “Fenomenos homoclınicos en sistemas reversibles” (Talk). Nolineal 2000,Almagro, 31/may–3/jun 2000.

12. T.M. Seara, A. Delshams, R. de la Llave. “Orbitas con energıa no acotada en perturbaciones periodicasde flujos geodesicos en el toro” (Talk). Nolineal 2000, Almagro, 31/may–3/jun 2000.

13. T.M. Seara, J. Villanueva. “Matching complejo aplicado al estudio del dominio de analiticidad de lascurvas invariantes de la aplicacion Standard” (Talk). Nolineal 2000, Almagro, 31/may–3/jun 2000.

14. Yu. Fedorov. “Integrable discretizations of some problems of classical mechanics” (Invited Talk). 34thSymposium on Mathematical Physics, Nicolas Copernicus University, Torun, Polonia, jun 2000.

15. J.J. Morales. “Meromorphic Non-integrability of Hamiltonian Systems” (Invited Talk). The 32nd Sym-posium on Mathematical Physics, Institute of Physics, Nicolaus Copernicus University, Torun, Polonia,6–10 jun 2000.

16. J. Llibre, M. Olle. “Horseshoe periodic orbits for Saturn coorbital satellites” (talk). III Jornadas deMecanica Celeste, Monografıas del seminario matematico Garcıa de Galdeano, Valladolid, 8-9 Jun 2000.

17. E. Fontich, P. Martın. “Hamiltonian systems with orbits covering densely submanifolds of small codi-mension” (Poster). Third European Congress of Mathematics, Barcelona, 10–14 Jul 2000.

18. F. Gabern, A. Jorba. “Study of a model for the dynamics near the triangular points of the Sun-Jupitersystem” (Poster). Third European Congress of Mathematics, Barcelona 2000, Barcelona, 10–14 Jul 2000.

19. A. Gonzalez, A. Jorba, R. de la Llave, J. Villanueva. “On the Existence of an Invariant Torus Closeto a Quasi-Torus of an Exact Symplectic Map” (Poster). Third European Congress of Mathematics,Barcelona 2000, Barcelona, 10-14 Jul 2000.

20. A. Jorba, J. Villanueva. “The Fine Geometry of the Cantor Families of Invariant Tori in HamiltonianSystems” (Invited Talk). Third European Congress of Mathematics, Barcelona 2000. Mini-Symposiumon Symplectic and Contact Geometry and Hamiltonian Dynamics, Barcelona, 10–14 Jul 2000.

21. C. Olive, T.M. Seara. “Using Equational Resurgence In Hamilton–Jacobi Equation to Compute SplittingOf Separatrices In The Singular Case” (Poster). Third European Congress of Mathematics, Barcelona,10–14/jul 2000.

22. A. Guillamon, E. Freire, A. Gasull. “Vector fields in the plane with monotone periods” (Comunicacionoral). Third world congress of nonlinear analysts, WCNA-2000, Catania (Italia), Julio 19-26, 2000.

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23. J. Llibre, M. Olle. “Motion of the co-orbital satellites of Saturn in the Restricted three-body problem”(talk). NATO ASI The restless univers: applications of gravitational n-body dynamics to planetary,stellar and galactic dynamics, Blair Atholl, Escocia, 23 Jul al 5 Aug2000.

24. J.J. Masdemont, G. Gomez. “Heteroclinic Connections between Libration Point Orbits” (Invited Talk).SIAM Pacific Rim Dynamical Systems Conference, Marriot, Maui, Hawaii (USA), 9–13/ago 2000.

25. G. Gomez, M.W. Lo, J.J. Masdemont, K. Museth. “Simulation of Formation Flight Near L2 for the TPFMission” (). ASS/AIAA Space Flight Mechanics Conference. Paper AAS 01-305, Quebec City, Quebec,Canada, Agosto 2000.

26. J.J. Masdemont. “Formation Flight. Dynamics” (conferencia invitada). Lagrange Points & the Explo-ration of Space, Beckmann Institute Auditorium, Caltech (USA), 19/oct 2000.

27. R. de la Llave, A. Delshams, T.M. Seara. “Orbits of unbounded energy in geodesic flows and timedependent potential and in other mechanical systems” (Talk). 2000 Fall Southeastern AMS SectionMeeting, Birmingham, Alabama, USA, 10–12/nov 2000.

28. Yu. Fedorov. “Ellipsoidal billiards with separable potentials” (Talk). SIDE IV Meeting, Tokyo, Japon,18 a 25 nov 2000.

29. M.W. Lo, J.J. Masdemont. “Estimation of Formation Flight cost for TPF” (Invited Talk). TerrestrialPlanet Finder Working Group, Marriot, Pasadena (USA), 29/nov 2000.

30. A. Delshams, A. Guillamon, J.T. Lazaro. “An approach to the center-focus problem via pseudo normalforms” (conferencia invitada). Second Symposium on Planar Vector Fields, Lleida, 17–20 Dec 2000.

31. Yu. Fedorov. “Backlund transformations with several parameters” (Invited Talk). First Joint Interna-tional Meeting between the AMS and the HKMS, Hong Kong, China, Dic 2000.

32. J. Blasco, M. Espino, M.A. Maidana, P.S. Casas, M.A. Garcıa. “3D Computation of Plane Poiseuille flowusing a pressure stabilized, finite element formulation” (talk). Finite Elements in Flow Problems 2000,Austin (Texas, EEUU), 2000.

33. P.S. Casas, A. Jorba. “Numerical study of bifurcations for the two-dimensional Poiseuille flow” (Poster).8th European Turbulence Conference, Barcelona, 2000.

34. D. Gomez-Ullate, A. Gonzalez-Lopez, M.A. Rodrıguez. “New algebraic many-body problems” (PonenciaInvitada). NEEDS (Non-linear Evolution Equations and Dynamical Systems), Gokova, Turkey, 2000.

35. R. de la Llave. “De como ganar mucha energıa haciendo poca fuerza” (Invited Talk). I Meeting of theRSME, Madrid, 2000.

36. R. de la Llave. “Geometric mechanisms for orbits of unbounded energy in periodic perturbations” (InvitedTalk). Dynamical Systems meeting, Maryland, 2000.

37. R. de la Llave. “Arnol’d diffusion” (plenary talk). Dynamical Systems meeting, Edinburgh, 2000.38. R. de la Llave. “Geometric mechanisms for diffusion in Hamiltonian mechanics” (Talk). Southwest

regional meeting, Los Angeles, 2000.39. Ch. Pantazi. “Distance Geometry of Molecule” (participacion en un proyecto). ECMI modelling Week,

Lund, Suecia, 2000.

YEAR 2001

40. J.J. Morales. “Differential Galois Theory and Chaotic Dynamics” (Invited Talk). Conference on Differ-ential equations in the Complex Domain, Universite Louis Pasteur, Strasbourg, Francia, 1–6 feb 2001.

41. A. Delshams, R. de la Llave, T.M. Seara. “A geometric mechanism for diffusion in Hamiltonian systems”(conferencia invitada). Fourth International Symposium on Hamiltonian Systems and Celestial Mechanics(HAMSYS 2001), Guanajuato, Mexico, 19–24/mar 2001.

42. A. Gonzalez, A. Jorba, R. de la Llave, J. Villanueva. “On the Existence of a Family of Invariant ToriClose to a Quasi-Torus of an Exact Symplectic Map” (talk). IV International Symposium and Workshopon Hamiltonian Systems and Celestial Mechanics (HAMSYS 2001), Guanajuato, Mexico, 19–24 Mar2001.

43. A. Jorba, F. Gabern. “Restricted Four-Body models for the dynamics of the Trojan asteroids” (InvitedTalk). IV International Symposium and Workshop on Hamiltonian Systems and Celestial Mechanics(HAMSYS 2001), Guanajuato, Mexico, 19–24 Mar 01.

44. R. de la Llave. “Aubry-Mather theory for minimal surfaces” (Talk). HAMSYS 2001, Guanajuato,Mexico, 19–24/mar 2001.

33

45. J. Llibre, M. Olle. “Horseshoe periodic orbits in the Restricted three-body problem” (talk). IV Inter-national Symposium and Workshop on Hamiltonian Systems and Celestial Mechanics (HAMSYS 2001),Guanajuato, Mexico, 19–24 Mar de 2001.

46. M. Olle, J.R. Pacha, J. Villanueva. “On Bifurcations Linked to Transitions Stable–Complex Unstable inThree Degrees of Freedom Hamiltonian Systems” (talk). IV International Symposium and Workshop onHamiltonian Systems and Celestial Mechanics (HAMSYS 2001), Guanajuato, Mexico, 19–24 Mar 2001.

47. A. Delshams, J.T. Lazaro. “Pseudo-normal forms and their applications” (Talk). Symmetry and Pertur-bation Theory, SPT 2001, Cala Gonone, Sardinia, Italia, 6–13/may 2001.

48. J.J. Morales. “The Poincare-Arnold-Melnikov integral and the Differential Galois Theory” (Invited Talk).Singularities of Differential Equations and Foliations, CMAF, Lisboa, Portugal, 7–12 may 2001.

49. T.M. Seara, A. Delshams, R. de la Llave. “Overcoming the Large Gap Problem” (Invited Talk). SixthSIAM Conference on Applications of Dynamical Systems (DS01), Snowbird, Utah, USA, 20–24/may2001.

50. J.J. Morales. “Differential Galois Theory and bifurcation of asymptotic surfaces” (Invited Talk). Differ-ential Galois Theory, The Mathematical Conference Center (Banach Center), Bedlewo, Poland, 28/may–1/jun 2001.

51. F. Gabern, A. Jorba. “On the triangular points of the Sun-Jupiter system” (talk). Third Meeting onCelestial Mechanics (CELMEC III), Monte Porzio Catone, Roma, Italia, 18–22 junio de 2001.

52. M. Olle, J.R. Pacha, J. Villanueva. “Estimates and Intricacities of the Normalized Hamiltonian Neara Critical Periodic Orbit” (talk). Third Meeting on Celestial Mechanics (CELMEC III), Monte PorzioCatone, Roma, Italia, 18–22 Jun 2001.

53. S. Bolotin, A. Delshams, Yu. Fedorov, R. Ramırez Ros. “Homoclinic and heteroclinic billiard orbitsinside perturbed ellipsoids” (Invited Talk). Progress in Nonlinear Science, Nizhny Novgorod, Rusia,2–6/jul 2001.

54. M. Olle, J.R. Pacha, J. Villanueva. “On the Hamiltonian Andronov-Hopf Bifurcation” (talk). Progressin Nonlinear Science, Nizhny Novgorod, Rusia, 2–6 Jul 2001.

55. A. Guillamon, D.W. McLaughlin, J. Rinzel. “Estimation of conductances in primary visual cortex”(Comunicacion oral). Sloan-Swartz Summer Meeting, Lake Tahoe (California, EEUU), Julio 14-19, 2001.

56. G. Gomez, W. Koon, M.W. Lo, J.J. Masdemont, J. Marsden, S. Ross. “Invariant Manifolds and MaterialTransport in the Solar System” (Invited Talk). AAS/AIAA Astrodynamics Specialists Conference, Hilton,Quebec (Canada), 30/jul–2/ago 2001.

57. G. Gomez, W. Koon, M.W. Lo, J.J. Masdemont, K. Museth. “Simulation of Formation Flight near L2

for the TPF Mission” (Invited Talk). AAS/AIAA Astrodynamics Specialists Conference, Hilton, Quebec(Canada), 30/jul–2/ago 2001.

58. G. Gomez, J.J. Masdemont, R. Shope. “The Interplanetary Superhighway System of the Future” (In-vited Talk). The Biennal Conference of the World Council for Gifted and Talented Children. KeynotePresentation, Gran Salon Barcelona. Barcelo Hotel Sants, Barcelona, 31/jul–4/ago 2001.

59. W. Koon, J. Marsden, J.J. Masdemont, R. Murray. “J2 Dynamics and Formation Flight” (Talk). AIAAGuidance Navigation and Control Conference, Montreal (Canada), 6–9/ago 2001.

60. J.J. Morales. “No integrabilidad meromorfa de sistemas hamiltonianos: teorıa” (Invited Talk). IV Jor-nadas de Mecanica Celeste, Universidad de Murcia – Universidad de Cartagena, 20–22/set 2001.

61. J.J. Morales. “No integrabilidad meromorfa de sistemas hamiltonianos: aplicaciones” (Invited Talk).IV Jornadas de Mecanica Celeste, Universidad de Murcia – Universidad de Cartagena, 20–22/set 2001.

62. M. Olle, J.R. Pacha, J. Villanueva. “Confinement Around the Vertical Family of Periodic Orbits Close tothe Lagrangian Points L4 and L5 in the 3D RTBP” (talk). IV Jornadas de Trabajo en Mecanica Celeste,La Manga del Mar Menor, Murcia, del 20–22 Set 2001.

63. P.S. Casas, A. Jorba. “Unstable quasi-periodic solutions for the 2-D Poiseuille problem” (talk). XVIICEDYA/VII Congreso de Matematica Aplicada, Salamanca, 2001.

64. A. Delshams, R. de la Llave, T.M. Seara. “How to increase the energy (in a geodesic flow) with asmall (quasiperiodic) forcing” (Talk). XVII CEDYA/VII Congreso de Matematica Aplicada, Salamanca,24–28/sep 2001.

65. F. Gabern, A. Jorba. “Sobre los puntos Lagrangianos del sistema Sol-Jupiter” (talk). XVII CEDYA /VII CMA, Salamanca, 24–28 Set 2001.

66. A. Jorba, A. Gonzalez, R. de la Llave, J. Villanueva. “Teorıa K.A.M. sin Coordenadas Accion–Angulo”(Talk). XVII CEDYA/VII Congreso de Matematica Aplicada, Salamanca, 24–28/sep 2001.

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67. C. Olive, T.M. Seara. “Resurgencia ecuacional en el estudio de una ecuacion de Hamilton–Jacobi” (Talk).XVII Congreso de Ecuaciones Diferenciales y Aplicaciones, Salamanca, 24–28/sep 2001.

68. R. Ramırez Ros. “Trayectorias periodicas de billares en circunferencias perturbadas” (Talk). XVIICEDYA/VII CMA, Salamanca, 24–28/sep 2001.

69. J.J. Masdemont. “Finance related to Stochastic behavior and Risk” (Invited Talk). Information Networksand Systems Technologies, Belarus State Economic University, Minsk, Belarus, 2–4/oct 2001.

70. G. Gomez, W.S. Koon , M. Lo, J.J. Masdemont, J. Marsden , S. Ross. “Invariant Manifolds, the Three-Body Problem and a Petit Grand Tour of Jovian Moons” (talk). IMA Workshop 3. Dynamical Systems inCelestial Mechanics and Climate Dynamics, University of Minnesota, Minneapolis, USA, 29 Oct 2001–2Nov 2001.

71. J.J. Morales. “The Poincare-Arnold-Melnikov integral and the differential Galois theory” (Invited Talk).Journees hamiltoniennes, Universite de Montpelier II, 22–24/nov 2001.

72. A. Jorba, F. Gabern. “Models for the dynamics of the Trojan asteroids” (Invited Talk). Workshop onComputational Challenges in Dynamical Systems, Fields Institute, Toronto, Canada, 3–7 Dec 2001.

73. D. Gomez-Ullate, F. Finkel, A. Gonzalez-Lopez, M.A. Rodrıguez. “Modelos de Calogero–Sutherland yoperadores de Dunkl” (). X Encuentro de Geometrıa y FYsica, Miraflores de la Sierra, Madrid, 2001.

74. D. Gomez-Ullate. “An-type Dunkl operators and new spin Calogero–Sutherland models” (). TheCalogero-Moser system 30 years later, Roma, 2001.

75. R. de la Llave. “Several geometric mechanism for diffusion” (Talk). 4th Workshop in nonlinear dynamicsand chaos, New York, 2001.

76. R. de la Llave. “Partial differential equations in periodic media” (Invited Talk). Arkansas Spring Lecture,Fayetville, 2001.

77. R. de la Llave. “Smooth classification of dynamical systems” (Invited Talk). CBMS lectures, Columbia,2001.

YEAR 2002

78. T.M. Seara, A. Delshams, R. de la Llave. “Arnold Diffusion: Overcoming the large gaps problem” (Talk).Workshop on Hamiltonian Dynamical Systems, Imperial College, London, 11–15/feb 2002.

79. R. de la Llave, A. Delshams, T.M. Seara. “Geometric mechanisms for diffusion in mechanical systems”(Talk). 976 AMS Meeting, Montreal, Quebec, Canada, 3–5/may 2002.

80. Yu. Fedorov. “Steklov–Lyapunov type systems and their integrable discretizations” (Invited Talk).Symmetries and Perturbation Theory SPT2002, Cala Gonone, Sardenya, Italia, 19–26/may 2002.

81. N. Fagella, T.M. Seara, J. Villanueva. “Limits of Herman Rings of the Complex Standard Family”(Invited Talk). Holomorphic Iteration and Non-Uniform Hyperbolicity, Varsovia, Polonia, 22–26/may2002.

82. A. Delshams, R. de la Llave, Tere M. Seara. “Geometric methods for instability in Hamiltonian systems”(Conferencia invitada). The Fourth International Conference on Dynamical Systems and DifferentialEquations, Wilmington, NC, USA, 24 al 27 May 2002.

83. G. Gomez, J.J. Masdemont. “Analisis de Misiones Espaciales” (Invited Talk). No Lineal 2002, U. deCastilla – La Mancha, Cuenca, 5–8/jun 2002.

84. A. Guillamon, D.W. McLaughlin, J. Rinzel. “Estimacion de conductancias e implicaciones en la estruc-tura sinoptica” (Comunicacion oral). No Lineal 2002, Cuenca, Junio 5-8, 2002.

85. P. Gutierrez, A. Delshams, T.M. Seara. “Splitting exponencialmente pequeno y continuacion de latransversalidad en un sistema hamiltoniano” (Talk). No Lineal 2002, Cuenca, 5–8/jun 2002.

86. R. de la Llave, A. Delshams, T.M. Seara. “Metodos geometricos para la inestabilidad en sistemas hamil-tonianos” (Invited Talk). No-lineal 2002, U. de Castilla – La Mancha, Cuenca, 5–8/jun 2002.

87. J. Llibre and Ch. Pantazi. “New results on the Darbouxian Theory of integrability for planar polynomialdifferential systems” (talk). Nolineal 2002, Cuenca, 5–8 Jun 2002.

88. C. Olive, D. Sauzin and T.M. Seara. “Existencia de soluciones resurgentes de una ecuacion en derivadasparciales” (talk). Nolineal 2002, U. de Castilla-la Mancha, Cuenca, 05-08 junio, 2002.

89. P. Roldan, A. Delshams. “Parallel implementation of a Lie series algorithm for computing normal forms”(talk). No Lineal 2002, Cuenca, 5 May–8 Jun 2002.

90. J. Cobos, J. Masdemont. “Astrodynamical Applications of Invariant Manifolds associated with CollinearLissajous Libration Orbits” (Talk). Libration Point Orbits and Applications, Aiguablava, 10–14/jun 2002.

35

91. F. Gabern, A. Jorba. “Restricted four and five body problems in the Solar System” (talk). LibrationPoint Orbits and Applications, Parador d’Aiguablava, Girona, 10–14 Jun 2002.

92. G. Gomez, W.S. Koon, M.W. Lo, J. Marsden, J.J. Masdemont, S.D. Ross. “Invariant Manifolds, theSpatial Three-Body Problem and Petit Grand Tour of Jovian Moons” (Invited Talk). InternationalConference on Libration Point Orbits and Applications, Parador d’Aiguablava, Girona, Junio 2002.

93. G. Gomez, M. Marcote, J.J. Masdemont. “Trajectory Correction Maneuvers in the Transfer to LibrationPoint Orbits” (Talk). Libration Point Orbits and Applications, Aiguablava, 10–14/jun 2002.

94. G. Gomez, J.J. Masdemont. “Libration Point Orbits. A Survey from the Dynamical Point of View”(Invited Talk). Libration Point Orbits and Applications, Aiguablava, 10–14/jun 2002.

95. G. Gomez, J.J. Masdemont, J.M. Mondelo. “Dynamical Substitutes of the Libration Points for SimplifiedSolar System Models” (Talk). Libration Point Orbits and Applications, Aiguablava, 10–14/jun 2002.

96. F. Gabern, A. Jorba. “Some models for the Trojan motion” (talk). V Jornadas de Mecanica Celeste,Albarracın, Teruel, 19–21 junio de 2002.

97. M. Olle, J. R. Pacha, J. Villanueva. “On Resonant and Nonresonant Normal Forms” (talk). V Jornadasde Mecanica celeste, Albarracın, Teruel, 19–21 Jun 2002.

98. C. Olive, D. Sauzin and T.M. Seara. “Two examples of resurgence” (Talk). Singularites, equationsdifferentielles et aspects mathematiques de la physique quantique. Colloque en l’honneur de F. Pham,Lab. J.A. Dieudonne, Sophia-Antipolis Univ., 3–5/jul 2002.

99. Yu. Fedorov. “Integrable nonholonomic systems on Lie groups” (Invited Talk). Workshop ‘Geometry,Symmetry and Mechanics II’, University of Warwick, Reino Unido, 22–26/jul 2002.

100. A. Delshams, P. Gutierrez and T.M. Seara. “Exponentially small splitting of separatrices for whiskeredtori in Hamiltonian systems” (Invited Talk). Workshop on Differential Equations dedicated to the memoryof V. Lazutkin, San Petersburgo, Rusia, 18–20/ago 2002.

101. Yu. Fedorov. “Ellipsoidal billiards with separable potentials” (Talk). Workshop on Differential Equationsdedicated to the memory of V. Lazutkin, Mathematical Steklov Institute, San Petersburgo, Rusia, 18–20/ago 2002.

102. R. Ramırez Ros. “Exponentially small separatrix splitting for billiards inside perturbed almost-circularellipses” (Talk). Workshop on Differential Equations dedicated to the memory of V. Lazutkin, San Petes-burgo, Rusia, 18–20/ago 2002.

103. N. Fagella, T.M. Seara, J. Villanueva. “Asymptotic Size of Herman Rings of the Complex StandardFamily” (Talk). International Conference on Dynamical Methods for Differential Equations (dmde’02),Medina del Campo, Valladolid, 4–7/sep 2002.

104. F. Gabern, A. Jorba. “Restricted four and five body problems in the Solar System” (talk). InternationalConference on Dynamical Methods for Differential Equations (dmde’02), Medina del Campo, Valladolid,4–7 Sep de 2002.

105. R. de la Llave, A. Delshams, T.M. Seara. “Geometric mechanisms for topological instability in Hamilto-nian Systems” (Invited Talk). International Conference on Dynamical Methods for Differential Equations(Dmde’02), Medina del Campo, Valladolid, 4–7/sep 2002.

106. J. Puig, C. Simo. “Hill’s equation with quasi-periodic forcing: resonance tongues and reducibility” (Talk).Dynamical methods for Differential Equations, Medina del Campo, Valladolid, 4–7 sep 2002.

107. Yu. Fedorov. “Integrable nonholonomic systems on Lie groups” (Talk). Classification Problems in theTheory of Integrable Systems, SISSA – Trieste, Italia, 1–5/oct 2002.

108. C. Beichman, G. Gomez, M. Lo, J.J. Masdemont, L. Romans. “Searching for Life with the TerrestrialPlanet Finder: Lagrange Point Options for a Formation Flying Interferometer” (talk). 53rd InternationalAstronautical Congress IAF-POSPAR, G.R. Brown Convention Center, Houston, TX, USA, 10–18 Oct2002.

109. C. Olive, D. Sauzin and T.M. Seara. “Existence of resurgent solutions in a partial differential equation”(Invited Talk). Resurgence, Alien Calculus, Resummability, Transseries, CIRM, Marseille-Luminy, 18–22/nov 2002.

110. A. Delshams, R. de la Llave, T.M. Seara. “Geometric mechanisms for instability in Hamiltonian dynam-ical systems” (Talk). AMS sectional meeting, Wisconsin, 2002.

111. R. de la Llave. “A gradient flow approach quasi-periodic solutions for P.D.E’s and Ψ-D.E.’s” (Talk).AMS sectional meeting, Wisconsin, 2002.

112. D. Gomez-Ullate. “Generalizing Calogero–Sutherland models” (Ponencia Invitada). Scientific Gatheringon Integrable Systems, CiC Cuernavaca, Mexico, 2002.

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113. R. de la Llave. “Geometric mechanisms for diffusion in mechanical systems” (Invited Talk). Regionalmeeting of the AMS, Montreal, 2002.

114. R. de la Llave. “Geometric mechanisms for instability in Hamiltonian mechanics” (Invited Talk). Con-ference in honor of J. Mather, Princeton, 2002.

115. C. Olive, D. Sauzin, T.M. Seara. “Two examples of resurgence” (Invited Talk). Analyzable functionsand applications, Edimburgh, 2002.

116. C. Olive, D. Sauzin, T.M. Seara. “Resurgence in Hamilton–Jacobi equation” (Invited Talk). Singularites,equations differentielles et aspects mathematiques de la physique quantique, Nice, 2002.

YEAR 2003

117. J.J. Masdemont. “Orbital Mechanics and Perturbations” (Invited Talk). Communication Satellites:Discover the key of global connectivity (BEST-IEEE), UPC, Barcelona, 23–30 MaMar 003.

118. R. de la Llave, A. Delshams, T.M. Seara. “A Rigorous Proof of the Existence of Diffusion in a Problemwith Large Gaps” (Invited Talk). Workshop on Hamiltonian Dynamics, Georgia Tech, Atlanta, EEUU,5–6 Abr 2003.

119. P. Acosta-Humanez. “Some Homomorphisms in discrete dynamical systems” (talk). Dynamical Systems,Denton, Texas, 2003.

120. A. Delshams, R. de la Llave, T.M. Seara. “Orbits of unbounded energy in generic quasi-periodic per-turbations of geodesic flows for certain manifolds” (Invited Talk). Dynamical Systems, Denton, Texas,25–29 May 2003.

121. A. Delshams, R. de la Llave, T.M. Seara. “Geometric mechanism for instability in Hamiltonian systems”(Conferencia invitada). Dynamical Systems, Denton, Texas, 25–29 May 2003.

122. R. de la Llave. “Geometric methods in Arnold diffusion” (Plenary speaker). Dynamical Systems, Denton,TX, 2003.

123. S. Bolotin, A. Delshams, R.Ramırez Ros. “Persistence of heteroclinic orbits for billiards and twist maps”(Conferencia invitada). SIAM Conference of Applications of Dynamical Systems (DS03), Snowbird, Utah(EEUU), 27–31 May 2003.

124. A. Delshams, R. de la Llave, T.M. Seara. “Diffusion in Hamiltonian systems using geometrical methods”(Conferencia invitada). SIAM Conference of Applications of Dynamical Systems (DS03), Snowbird, Utah(EEUU), 27–31 May 2003.

125. D. Gomez-Ullate, A.N.W. Hone and M. Sommacal. “Numerical integration of a many body problemin the plane. A customer’s review” (Ponencia invitada). Workshop on Group Theory and NumericalMethods, Centre de Recherches Mathematiques, Montreal, 28 mayMay 03.

126. R. de la Llave. “Semiclassical methods” (Lectures). Computational Chemistry workshop, Barcelona,2003.

127. P. Roldan, A. Delshams, R. de la Llave. “Numerical computation of the scattering map” (talk). COCHEM2003 - Nonlinear phenomena in computational chemical physics, Universitat de Barcelona, 9–14 Jun 2003.

128. D. Gomez-Ullate. “Classical many-body problems with periodic and chaotic orbits” (Poster). QuantumChaos: Theory and applications, Villa Olmo, Como (Italia), 18 Jun 2003.

129. S. Bolotin, A. Delshams, R.Ramırez Ros. “Persistence of homoclinic orbits for billiards and twist maps”(Conferencia invitada). First Joint Meeting RSME–AMS, Sevilla, 18–21 Junio 2003.

130. A. Delshams, R. de la Llave, T.M. Seara. “Geometric mechanisms for diffusion in Hamiltonian Systems”(Conferencia invitada). First Joint Meeting RSME–AMS, Sevilla, 18–21 Junio 2003.

131. A. Delshams, R. de la Llave, T.M. Seara. “A geometric mechanism for diffusion in Hamiltonian Systemsovercoming the large gaps problem” (Invited Talk). First Joint Meeting RSME–AMS, Sevilla, 18–21Junio 2003.

132. N. Fagella, T.M. Seara, J. Villanueva. “Quantitative Estimates on the Size of Herman Rings of theComplex Standard Family using Geometrical Methods” (Invited Talk). First Joint Meeting RSME–AMS, Special Session on Dynamical Systems, Sevilla, del 18–21 Jun 2003.

133. A. Jorba, M. Olle. “On the Hamiltonian-Hopf bifurcation” (talk). I Congreso RSME-AMS, Sevilla, del18–21 Jun 2003.

134. J.J. Morales. “Differential Galois Theory and Integrability” (Invited Talk). Primer Congreso conjuntoRSME-AMS, Universidad de Sevilla, 18–21 junio 2003.

37

135. N. Fagella, T.M. Seara, J. Villanueva. “Asymptotic Size of Herman Rings of the Complex StandardFamily” (Conferencia Invitada). Dynamics in the Complex Plane, an international symposium in honourof B. Branner, Sominestationen, Holbaek, Dinamarca, del 19–21 Jun 2003.

136. Yu. Fedorov. “Integrable discretizations of Steklov–Lyapunov type systems” (Talk). Symmetry inNonlinear Mathematical Physics 2003, Kiev, Ukraine, 23–29 de Junio de 2003.

137. S. Bolotin, A. Delshams, R.Ramırez Ros. “Persistence of ‘clinic’ orbits for twist maps and billiards”(Conferencia invitada). International Conference on Differential Equations (Equadiff 2003), Hasselt,Belgica, 22–26 Julio 2003.

138. H. Broer, H. Hanßmann, A. Jorba, J. Villanueva, F. Wagener. “Quasi–Periodic Response Solutions atNormal–Internal Resonances” (Invited Talk). Equadiff 2003, International Conference on DifferentialEquations, Mini–Symposia on Quasi–Periodicity, Hasselt, Belgica, del 22–26 Jul2003.

139. P.S. Casas, A. Jorba. “Unstable manifolds computation for the two-dimensional plane Poiseuille flow”(talk). EQUADIFF 2003, Hasselt (Belgica), 2003.

140. A. Delshams, R. de la Llave, T.M. Seara. “Geometric mechanisms for Arnold diffusion” (Invited talk).International conference of Differential equations, Equadiff-2003, Hasselt, Belgica, del 22–26 Jul2003.

141. A. Delshams, R. de la Llave, T.M. Seara. “Orbits of unbounded energy in generic quasi-periodic perturba-tions of geodesic flows” (Invited Talk). International conference of Differential equations, Equadiff-2003,Hasselt, Belgica, del 22–26 Jul2003.

142. A. Gonzalez, A. Jorba, R. de la Llave, J. Villanueva. “KAM Theory without Action–Angle Coordinatesas a Methodology for Proving Long Time Stability in Hamiltonian Systems” (Invited talk). Equadiff2003, International Conference on Differential Equations, Mini–Symposia on Quasi–Periodicity, Hasselt,Belgica, del 22–26 Jul de 2003.

143. R. de la Llave, E. Fontich, P. Martın. “Invariant pre-foliations for non-resonant non-uniformly hyperbolicsystems” (talk). Equadiff 2003, Hasselt, Belgica, 22–26 de julio de 2003.

144. J.J. Morales. “Differential Galois Methods in Celestial Mechanics” (Invited Talk). Equadiff 2003, Hasselt,Belgica, 22–26 julio 2003.

145. C. Olive, D. Sauzin, T.M. Seara. “Existence of Resurgent Solutions in a Nonlinear First Order PartialDifferential Equation” (talk). International conference of Differential equations, Equadiff-2003, Hasselt,Belgica, del 22–26 de julio de 2003.

146. J. Puig, C. Simo. “The spectrum of Schrodinger operators with quasi-periodic potential: a dynamicalapproach” (Conferencia invitada). International Conference on Differential Equations Equadiff 2003,Hasselt, Belgica, 22 al 26 Julio 2003.

147. S. Abenda, Yu. Fedorov. “Integrable billiards on quadrics and Poncelet theorem” (Talk). IntegrableSystems and Foliations, Lille, Francia, 23–29 Jul2003.

148. D. Gomez-Ullate. “Differential invariants and invariant differential equations” (Talk). Banff InternationalResearch Centre, Banff, Canada, Aug 2003.

149. J.J. Masdemont. “The role of Libration Point Orbits in the Solar System” (Invited Talk). 1st AuroraStudent Design Contest, UPC-Auditorium, Barcelona, 8–9 Sep 2003.

150. F. Gabern, A. Jorba. “Normal Form for a Quasi-Periodic Perturbation of the Sun-Jupiter RestrictedThree-Body Problem” (Talk). Chaotic Worlds: From Order to Disorder in Gravitational N-Body Dy-namical Systems. NATO Advanced Science Institute, Cortina d’Ampezzo, Italy, 8–20 Sep 2003.

151. M. Olle, J. R. Pacha, J. Villanueva. “Bifurcation close to the vertical family of periodic orbits of L4 forµ > µR” (Talk). NATO ASI Chaotic worlds, Cortina d’Ampezzo (Italia), del 8–20 Set de 2003.

152. P.S. Casas, A. Jorba. “Unstable manifolds computation for the 2-D plane Poiseuille flow” (Talk). XVIIICEDYA/VIII Congreso de Matematica Aplicada, Tarragona, 2003.

153. J.M. Cors, J. Llibre, M. Olle. “On the central configurations of the coorbital satellite problem” (Talk).XVIII CEDYA, VIII CMA, Tarragona, 15–19 Set 2003.

154. A. Delshams, R. de la Llave, T.M. Seara. “A geometric method for instability in Hamiltonian Systems”(Invited Talk). XVIII CEDYA / VIII CMA, Tarragona, 15–19 Sep 2003.

155. N. Fagella, T.M. Seara, J. Villanueva. “Tamano asintotico de los anillos de Herman de la familia estandarde Arnold” (Talk). XVIII Congreso de Ecuaciones Diferenciales y Aplicaciones / VIII CMA, Tarragona,15–19 Sep 2003.

156. F. Gabern, A. Jorba. “Normal Form for a Quasi-Periodic Perturbation of the Sun-Jupiter RestrictedThree-Body Problem” (talk). XVIII CEDYA / VIII CMA, Tarragona, Sep 2003.

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157. P. Gutierrez and A. Delshams. “Exponentially small transversality for homoclinic orbits of hyperbolictori with quadratic irrational frequencies” (Talk). XVIII CEDYA / VIII CMA, Tarragona, 15–19 Sep2003.

158. J. Puig, C. Simo. “Sobre el espectro del operador de Schrodinger con potencial cuasiperiodico” (Talk).XVIII CEDYA / VIII CMA, Tarragona, 15–19 Sep 2003.

159. R. Ramırez Ros. “Singular phenomena for convex billiard tables” (Talk). XVIII CEDYA/VIII CMA,Tarragona, 15–19 Sep 2003.

160. J.J. Morales. “Galois Differential Approach to Perturbation of Asymptotic Surfaces in HamiltonianSystems: Statements and Examples” (Invited Talk). International Conference on the occasion of the60th Anniversary of J.-P. Ramis, Universite Paul Sabatier, Toulouse, 22–26 Sep 2003.

161. J. Puig. “The Ten Martini Problem” (Conferencia plenaria). 2nd Network Meeting of the IHP network‘Mathematical Analysis of Large Quantum Systems’, Viena (Austria), 6 and 7 Dec 2003.

162. P. Acosta-Humanez. “An application of functional analysis in a predator-prey system” (Talk). FourthInternational Conference in Dynamic Systems and Applications, Atlanta, Georgia, 2003.

163. P.S. Casas, A. Jorba. “Unstable manifolds computation for the two-dimensional plane Poiseuille flow”(Talk). 13th International Couette Taylor Workshop, Barcelona, 2003.

164. A. Haro, R. de la Llave. “New mechanisms of lack of equipartion of energy” (poster). Dynamics Days,Mallorca, 2003.

165. A. Haro, R. de la Llave. “Manifolds on the verge of a hyperbolicity breakdown” (poster). DynamicsDays, Mallorca, 2003.

166. R. de la Llave. “Geometric methods in Arnold diffusion” (Invited Talk). Dynamics Days, Mallorca, 2003.167. R. de la Llave. “Aubry-Mather theory and Partial differential equations” (Lectures). Winter School in

non-linear PDE’s, Lisboa, Portugal, 2003.168. R. de la Llave. “Geometric mechanisms for instability in Hamiltonian systems” (Invited Talk). Dynamical

Systems, Oberwolfach, 2003.169. R. de la Llave. “Geometric methods in Arnold diffusion” (Talk). Dynamical Systems, Oberwolfach, 2003.170. R. de la Llave. “Introduccion a la teorıa KAM” (Lectures). X Escuela de Matematicas, Guanajuato,

2003.171. R. de la Llave. “Panorama de la publicacion electronica en matematicas” (). Curso de la Universidad de

Verano Electronic publication, El Escorial, 2003.

YEAR 2004

172. J. Puig. “The Ten Martini Problem” (Conferencia invitada). 110th Annual Meeting of the AmericanMathematical Society, Phoenix (USA), 7–10 Jan 2004.

173. F. Gabern, W.S. Koon, J.E. Marsden and S.D. Ross. “Transition State for the Rydberg Atom” (Poster).Institute for Collaborative Biotechnologies Workshop, UCSB, California, USA, Feb 2004.

174. P. Roldan, A. Delshams and R. de la Llave. “Numerical computation of the scattering map” (Talk). 2004Texas Dynamics Workshop, University of Houston, 26–27 Mar 2004.

175. D. Gomez-Ullate. “The direct approach to Quasi-exact solvability” (Ponencia Invitada). Symmetriesand perturbation theory, Cala Gonone, Italia, May 2004.

176. I. Baldoma, T.M. Seara. “Estudio de la ecuacion ‘inner’ en un problema de escision de separatricesexponencialmente pequeno en R3” (Talk). NoLineal 2004, Toledo, 1–4 Jun 2004.

177. E. Canalias, J.J. Masdemont. “Homoclinic and heteroclinic connections between Lyapunov orbits ofthe planar restricted three body problem” (Poster). No Lineal 2004, Universidad Castilla-La Mancha,Toledo, 1–4 Jun 2004.

178. P.S. Casas, A. Jorba. “Bifurcaciones de Hopf para diversos numeros de onda en el problema de Poiseuilleplano bidimensional” (Talk). Nolineal 2004: Nuevos retos y perspectivas en la dinamica no lineal and susaplicaciones, Toledo, 2004.

179. A. Gasull, A. Guillamon, E. Freire. “Isochrons, existence and stability of limit cycles through Lie sym-metries” (Comunicacion oral ). NoLineal 2004, Toledo, Junio 1-4, 2004.

180. A. Guillamon, G. Huguet. “Computacion efectiva de secciones isocronas usando simetrıas” (Poster).NoLineal 2004, Toledo, 1–4 Jun 2004.

181. J. Llibre and Ch. Pantazi. “Polynomial systems having a given Darbouxian function as a first integralor as an integrating factor” (Talk). Nolineal 2004, Toledo, 1–4 Jun 2004.

39

182. R. Ramırez Ros, S. Bolotin, A. Delshams. “Trayectorias homoclınicas de billares dentro de elipsoidesperturbados” (Talk). NoLineal 2004, Toledo, 1–4 Jun 2004.

183. P. Roldan, A. Delshams, R. de la Llave. “El ‘scattering map’ para variedades normalmente hiperbolicas”(Talk). NoLineal 2004, Toledo, 1–4 Jun 2004.

184. J.J. Morales. “A Remark about the Painleve Transcendents” (Invited Talk). Theories asymptotiques etequations de Painleve, Universidad de Angers (Francia), 1–5 Jun 2004.

185. S. Bolotin, A. Delshams and R. Ramırez Ros. “Persistence of homoclinic orbits for billiards inside per-turbed ellipsoids” (Talk). AIMS Fifth International Conference on Dynamical Systems and DifferentialEquations, Pomona, EEUU, 16–19 Jun 2004.

186. N. Fagella, T.M. Seara, J. Villanueva. “Quantitative Estimates on the Size of Herman Rings of theComplex Standard Family using Geometrical and Numerical Methods” (Invited Talk). AIMS FifthInternational Conference on Dynamical Systems and Differential equations, Cal Polytech, Pomona, CA(USA), 16–19 Jun 2004.

187. Yu. Fedorov, D. Zenkov. “Integrable discrete nonholonomic systems on Lie Groups” (Talk). AIMS FifthInternational Conference on Dynamical Systems and Differential equations, Pomona, CA, EE.UU., 16–19Jun 2004.

188. E. Fontich, P. Martın. “Hamiltonian systems with orbits covering densely submanifolds of small codi-mension” (Talk). AIMS Fifth International Conference on Dynamical Systems and Differential equations,Pomona, Estados Unidos, 16–19 Jun 2004.

189. F. Gabern, W.S. Koon and J.E. Marsden. “Spacecraft dynamics about an asteroid pair” (Talk). AIMS’Fifth International Conference on Dynamical Systems and Differential Equations, Pomona, California,USA, 16–19 Jun 2004.

190. P. Acosta-Humanez. “Polinomios exponenciales y la iteracion geometrica” (Talk). XXII Coloquio de laSociedad Matematica Peruana, Lima, Peru, 2004.

191. J.J. Morales. “Teorıa de Galois diferencial y no integrabilidad de Sistemas Hamiltonianos – I, II yIII” (3 conferencias invitadas). Coloquio de la Sociedad Matematica Peruana, Universidad Nacional deIngenierıa, Lima, Peru, 19 23 Jun 2004.

192. A. Gonzalez, A. Jorba, R. de la Llave, J. Villanueva. “A KAM Theorem for Quasiperiodic SymplecticMaps” (Talk). Workshop on Quasi-Periodic Dynamics, UB, Barcelona, 21 23 Jun 2004.

193. J. Llibre, M. Olle. “Central configurations for the n body problem” (Talk). VII Jornadas de mecanicaceleste, San Fernando (Cadiz), 28–30 Jun 2004.

194. A. Guillamon, M. Bruguera, A. Ferrer, M. Mitjana, F. Panyella, R. Perez, J.J. Rodrıguez, C. Serrat.“aCTeX: una eina telematica per a l’autoaprenentatge” (Poster). 3er congreso internacional de DocenciaUniversitaria e Innovacion, Girona, 30 Jun – 2 Jul , 2004.

195. G. Gomez, M.W. Lo, J.J. Masdemont. “Low Energy Transfers in the Solar System” (Lectures). SummerWorkshop on Advanced Topics in Astrodynamics, FME-Auditorium, Barcelona, 5–10 Jul 2004.

196. J.J. Masdemont, J.M. Mondelo. “Numerical and Analytical Techniques” (Lectures). Summer Workshopon Advanced Topics in Astrodynamics, FME-Auditorium, Barcelona, 5–10 Jul 2004.

197. J. Puig. “The Ten Martini Problem. Ideas and extensions” (Invited Talk). Spectral Theory of SchrodingerOperators, Montreal (Canada), 26–30 Jul 2004.

198. J.J. Morales. “Simetrıas en ecuaciones diferenciales” (Invited Talk). Primer Encuentro Internacional deMatematicas, Universidad Sergio Arboleda, Bogota, Colombia, 3 –6 Aug 2004.

199. J. Puig. “Cantor Spectrum for Quasi-Periodic Schrodinger Operators” (Invited Talk). Qmath9, Giens(Francia), 12–16 Set 2004.

200. E. Athanasoula, C.Garcıa-Gomez, J.J. Masdemont, M. Romero. “Formation Mechanism of Spiral Armsin Barred Galaxies” (Poster). Joint European and National Astronomical Meeting, Palacio de Congresosde Granada, 13–17 Set 2004.

201. Yu. Fedorov. “Algebraic closed geodesics on a triaxial ellipsoid” (Talk). Riemann–Hilbert problem andIntegrability, SISSA – Trieste, Italia, 20–24 Sep 2005.

202. J. Puig. “Reducibility of Quasi-Periodic Skew-Products and the Spectrum of Schrodinger Operators”(Invited Talk). Nonlinear Dynamics, Ergodic Theory and Renormalization, Leiden (Paises Bajos), 20–24Set 2004.

203. Yu. Fedorov. “Closed geodesics and billiards on quadrics related to elliptic KdV solutions” (InvitedTalk). Singularities and integrability of the Camassa-Holm equation, CIRAM – Bologna, Italia, 21–25Set 2004.

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204. J.J. Masdemont. “Aspectos Dinamicos del Diseno de Misiones Espaciales Relacionadas con Orbitas deLibracion” (Invited Talk). Dynamical Days 2004, Manga del Mar Menor, Murcia, 29 Set –1 Octubre2004.

205. J.J. Masdemont, E. Canalias. “Eclipse Avoidance for Lissajous Orbits using Invariant Manifolds” (Talk).55th International Astronautical Congress, Vancouver, Canada, 4–8 Oct 2004.

206. D. Gomez-Ullate. “Quasi-exact solvability beyond Lie algebras” (Invited Talk). Scientific meeting onIntegrable systems, CiC, Cuernavaca (Mor.), Mexico, Nov 2004.

207. J.J. Masdemont. “The Role of Invariant Manifolds in some Aspects of Libration Point Mission Design”(Invited Talk). XII Coloquio Brasileiro de Dinamica Orbital, Ubatuba-SP, Brazil, 29 Nov –3 Dec 2004.

208. J. Puig. “The Ten Martini Problem” (Conferencia plenaria). Journee Dynamique de l’Institut de Ma-thematiques de Jussieu, Parıs (Francia), 3 Dec 2004.

209. J.J. Masdemont. “Fundamentals of Dynamics and Applications of Libration Point Orbits” (Lectures).Workshop at INPE, Instituto Nacional de Pesquisas Espaciais (INPE), San Jose dos Campos, Brazil,7–10 Dec 2004.

210. R. de la Llave. “Plane-like critical points that are not minimizers in periodic variational problems” (Talk).2004 Spring Eastern Section Meeting of the AMS, Lawrenceville, 2004.

211. R. de la Llave. “The obstruction criterion for non existence of invariant circles and renormalization”(Talk). Joint meeting AMS-SMM, Houston, 2004.

212. R. de la Llave. “Geometric methods in Arnold diffusion” (Invited Talk). Workshop in HamiltonianMechanics and Partial Differential Equations, Montreal, 2004.

213. R. de la Llave. “Geometric methods in Arnold diffusion” (Invited Talk). Clay Mathematics Institute andMSRI Conference on Recent Progress in Dynamics, Berkeley, 2004.

YEAR 2005

214. A. Delshams, R. de la Llave, T.M. Seara. “Arnold Diffusion in Near Integrable Hamiltonian Systems”(Invited Talk). Pan-American Advanced Studies Institute 2005-Americas VI, Santiago de Chile, 10–21Jan 2005.

215. R. de la Llave. “Minimizers of periodic variational problems” (Lectures). Pan-American Advanced StudiesInstitute, Santiago de Chile, 2005.

216. F. Gabern. “Frequency analysis and the Trojan asteroids problem” (Lectures). Recent Trends in Non-linear Science, Castello, 24–28 Jan 2005.

217. A. Delshams, R. de la Llave, T.M. Seara. “A geometric method for instability in Hamiltonian systems”(Invited Talk). Dynamics, Bifurcation and Chaos. International conference dedicated to 70th anniversaryof L.P. Shilnikov, Nizhny Novgorod (Rusia), 30 Jan–4 Feb 2005.

218. J. Puig. “El Problema de los 10 Martinis” (Invited Talk). Congreso MAT.ES (RSME-SCM-SEIO-SEMA), Valencia, 31 Jan –4 Feb 2005.

219. Yu. Fedorov, D. Zenkov. “Continuous and Discrete nonholonomic systems on Lie Groups” (). CRMResearch Thematic Trimester on Control, Geometry and Engineering, Barcelona, 11 Feb 2005.

220. L. Garcıa, J.J. Masdemont. “Optimal Reconfiguration of Spacecraft Formations Using a Variational Nu-merical Method” (Talk). 4th International Workshop on Satellite Constellations and Formation Flying,Instituto Nacional de Pesquisas Espaciais (INPE), San Jose dos Campos, Brazil, 14–16 Feb 2005.

221. D. Gomez-Ullate. “From isochronicity to chaos” (Invited Talk). Calogero 70, Roma La Sapienza, Italia,febrero 2005.

222. A. Jorba and F. Gabern. “Numerical Approximation of the Dynamics around a Two-Torus of a Hamil-tonian System” (Conferencia Invitada). Qualitative Numerical Analysis of High-dimensional NonlinearSystems, Bristol, Gran Bretana, 21–24 Mar 2005.

223. A. Delshams, R. de la Llave, T.M. Seara. “Mechanisms of diffusion in near integrable Hamiltoniansystems” (Invited Talk). Saarifest. International conference dedicated to 65th anniversary of D. Saari,Guanajuato, Mexico, 3–9 Abr 2005.

224. J.J. Morales. “Non-integrability of some problems in Celestial Mechanics: a differential Galois approach”(Invited Talk). 2005 Spring AMS Central Section Meeting, Lubbock, Texas, USA, 8–10 Abr 2005.

225. J.J. Masdemont. “Analisis de Mision a los Puntos de Libracion” (Invited Talk). Jornadas CientıficasRSME: Matematicas y Analisis de Misiones Espaciales, Aula Magna, Universitat de Barcelona, 7 Jun2005.

41

226. E. Barrabes, M. Olle. “Horseshoe motion in the Restricted three-body problem” (Talk). VIII Jornadasde mecanica celeste, Rianxo (Galicia), 27–29 Jun 2005.

227. J.M. Cors, J. LLibre, M. Olle. “Configuraciones centrales del problema de los satelites coorbitales conmasas arbitrarias” (Talk). VIII Jornadas de mecanica celeste, Rianxo (Galicia), 27–29 Jun 2005.

228. J.J. Masdemont. “Formation Flight” (Lectures). 6th CVA Summer School. Community of Ariane Cities,CosmoCaixa, Barcelona, 18 Jul –12 Aug 2005.

229. J.J. Masdemont. “Libration Point Orbits” (Lectures). 6th CVA Summer School. Community of ArianeCities, CosmoCaixa, Barcelona, 18 Jul –12 Aug 2005.

230. G. Gomez, M.W. Lo, J.J. Masdemont. “A Control Procedure for the Station Keeping and FormationMaintenace of the TPF Mission” (Talk). 2005 AAS/AIAA Astrodynamics Specialist Conference, EmbassySuites Lake Tahoe Resort, Lake Tahoe, CA, USA, 7–11 Aug 2005.

231. G. Gomez, J.J. Masdemont, M. Marcote, J.M. Mondelo. “Natural Configurations and Control StrategiesSuitable for Formation Flying” (Talk). 2005 AAS/AIAA Astrodynamics Specialist Conference, EmbassySuites Lake Tahoe Resort, Lake Tahoe, CA, USA, 7–11 Aug 2005.

232. F. Angulo, E. Fossas, T.M. Seara. “Applied perturbation Theory to power converters regulation” (InvitedTalk). ENOC-2005, Eindhoven, Netherlands, 7–12 Aug 2005.

233. J.J. Masdemont. “Semi-Analytical Computations of Invariant Manifolds of Libration Point Orbits andtheir Applications in Libration Point Mission Design” (Invited Talk). Fifth EUROMECH NonlinearDynamics Conference (ENOC-2005), Eindhoven University of Technology, Eindhoven, Nederland, 7–12Aug 2005.

234. R. Ramırez Ros. “Exponentially small phenomena in some billiard tables” (Invited Talk). Fifth EU-ROMECH Nonlinear Dynamics Conference, Eindhoven, Holanda, 7–12 Aug 2005.

235. P. Acosta-Humanez. “El teorema de Morales–Ramis y el Algoritmo de Kovacic” (Invited Talk). XVCongreso Nacional de Matematicas, Bogota, Colombia, 8–12 Aug 2005.

236. P. Acosta-Humanez. “Genealogıa de Permutaciones Simples con orden una potencia de dos” (Talk).XV Congreso Nacional de Matematicas, Bogota, Colombia, 8–12 Aug 2005.

237. T.M. Seara. “Introduccion a la Teorıa de la Resurgencia” (Lectures). XV Congreso Nacional de Mate-maticas, Bogota, Colombia, 8–12 Aug 2005.

238. J. Villanueva. “Introduccio al Teorema KAM – I, II y III” (Lectures). XV Congreso Nacional deMatematicas. Sociedad Colombiana de Matematicas 50 anos, Hotel Tequendama, Bogota (Colombia),8–12 Aug 2005.

239. J.J. Masdemont. “Orbites i Trajectories” (Invited Talk). Commemoracio Any Mundial de la Fısica 2005,Agrupacio Astronomica de Manresa, 10 Sep 2005.

240. E. Barrabes, M. Olle. “Horseshoe motion in the Restricted three-body problem” (Talk). Celmec IV, S.Martino al Cimino (Italia), 11–15 Set 2005.

241. A. Delshams, G. Huguet. “The large gap problem in Arnold diffusion for non polynomial perturbationsof an a-priori unstable Hamiltonian system” (Poster). Fourth Meeting on Celestial Mechanics-CELMECIV, San Martino–Cimino (Viterbo), Italia, del 11–16 Set 2005.

242. P. Roldan, E. Canalias, A. Delshams, J.J. Masdemont. “On the scattering map and homoclinic connec-tions between Lyapunov orbits” (Talk). CELMEC IV – International Meeting on Celestial Mechanics,San Martino–Cimino (Viterbo, Italia), 11–16 Set 2005.

243. J.J. Masdemont. “Libration Point Dynamics and Methodologies with Applications to Space MissionDesign” (Invited Talk). EMS-SMC Mathematical Weekend, Universitat de Barcelona, 16–18 Sep 2005.

244. A. Delshams, J.T. Lazaro. “Forma Pseudo-normal: entre la forma normal de Birkhoff y la de Poincare-Dulac” (talk). XIX CEDYA / IX CMA, Leganes, 19–23 Sep 2005.

245. J. Puig. “Resultados no perturbativos en teorıa KAM” (Invited Talk). XIX CEDYA / IX CMA, Leganes,19–23 Sep 2005.

246. I. Baldoma, T.M. Seara. “Exponentially small splitting of heteroclinic orbits in a family in R3 ” (talk).International Conference of non-autonomous and stochastic Dynamical Systems, Sevilla, 27 Sep a 1octubre 2005.

247. A. Delshams, G. Huguet. “The large gap problem in Arnold diffusion for non polynomial perturbationsof an a-priori unstable Hamiltonian system” (talk). Non-autonomous and Stochastic Dynamical Systems(NSDS05), Sevilla, del 27 de Sep –1 de Octubre de 2005.

248. A. Delshams, R. de la Llave, T.M. Seara. “The scattering map to a normally hyperbolic invariantmanifold” (Conferencia invitada). NSDS05: International Conference of non-autonomous and stochasticDynamical Systems, Sevilla, 27 Sep –1 Octubre 2005.

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249. E. Canalias, J.J. Masdemont. “Lunar Gateway Station for providing services to Solar Libration pointmissions” (talk). 56th International Astronautical Federation Congress, Fukuoka (Japan), 17–21 Octubre2005.

250. F. Gabern, W.S. Koon, J.E. Marsden and S.D. Ross. “Application of Tube Dynamics to Non-statisticalReaction Processes” (Invited Talk). Critical Stability of Few-Body Quantum Systems, Max-Planck-Institute for the Physics of Complex Systems, Dresden, Alemania, 17–22 de octubre de 2005.

251. F. Gabern, W.S. Koon, J.E. Marsden and T. Yanao. “Dynamical systems approach to the Isomerizationproblem of a tri-atomic molecule” (talk). Critical Stability of Few-Body Quantum Systems, Max-Planck-Institute for the Physics of Complex Systems, Dresden, Alemania, 17–22 de octubre de 2005.

252. J. Puig. “Noperturbative Reducibility and Irreducibility” (Conferencia plenaria). Dynamics of Cocyclesand one-dimensional spectral theory, Oberwolfach (Alemania), 4–11 de noviembre 2005.

253. P.S. Casas, R. Quintanilla. “Numerical experiments on thermoelastic deformations in a rod with initialheat flux” (talk). Thermal Stresses 2005, Viena, 2005.

254. R. de la Llave. “Quasi-periodic orbits” (Lectures). Shoemaker lectures, Toledo, 2005.255. R. de la Llave. “Manifolds on the verge of a hyperbolicity breakdown” (Talk). Texas Dynamics Confer-

ence, San Antonio, 2005.256. R. de la Llave. “Geometric methods in Arnold diffusion” (Plenary lecture). 93 Conference in Statistical

Mechanics, Rutgers, 2005.257. R. de la Llave. “Invariant manifolds: rigorous results and computations” (Plenary lecture). SIAM

conference in applied dynamical systems, Snowbird, 2005.258. R. de la Llave. “Renormalization theory for noise” (Invited lecture). Workshop on Renormalization in

Dynamical Systems, Fields Institute, Toronto, 2005.

Stays (5 or more weeks long) and visits (less than 5 weeks long):

STAYS YEAR 2000

1. A. Delshams, Department of Mathematics, Univ. of Texas at Austin, Austin, Texas (USA), 2000, 5 se-manas. Transport and invariant objects in dynamical systems and applications.

2. Yu. Fedorov, Department of Mathematics, CIRAM – Universita degli studi di Bologna, Bologna (Italia),enero 2000, 5 semanas. Generalized Kowalevskaya–Painleve property.

3. Yu. Fedorov, School of Mathematics, University of Leeds, Leeds (Reino Unido), Abr 2000, 5 semanas.Backlund transformations of integrable flows on the loop algebra sl(n).

4. D. Gomez-Ullate, Universita di Roma III, Roma (Italia), may–sep 2000, 16 semanas. Colaboracion conO. Ragnisco.

5. A. Guillamon, Courant Institute of Mathematical Sciences, New York University, New York (EEUU),2000-01, 52 semanas. Modelos matematicos del cortex visual, neurociencia computacional.

6. R. de la Llave, Universitat Politecnica de Catalunya, Barcelona (Espana), jun–jul 2000, 8 semanas. .7. J. Masdemont, NASA-JPL, California Institute of Technology Caltech, Pasadena (USA), julio 2000,

22 semanas. Formation Flight around L2.8. J.J. Morales, Institut de Recherche Mathematique Avancee (IRMA), Universite Louis Pasteur, Estras-

burgo (Francia), Mar 2000, 5 semanas. Investigacion en teorıa de singularidades de ecuaciones diferen-ciales.

VISITS YEAR 2000

9. Yu. Fedorov, Departament de Matematica Aplicada II, UPC, Barcelona (Espana), 2000, 4 semanas.Backlund transformations of integrable flows.

10. J. Masdemont, JPL-Caltech, California Institute of Technology, Pasadena (USA), enero 2000, 2 semanas.LTool algorithm.

11. R. Ramırez-Ros, Instituto de Investigacion en Mat. Apl. y Sist., Univ. Nacional Autonoma de Mexico,Ciudad de Mexico (Mexico), 2000, 2 semanas. Transition chains in perturbed elliptic billiards.

12. R. Ramırez-Ros, Dep. of Mathematics, Univ. of Texas at Austin, Austin, Texas (USA), 2000, 1 semanas.Unbounded orbits for time-dependent billiards.

43

13. R. Ramırez-Ros, Dep. de Matematica Aplicada, Univ. de Granada, Granada (Espana), 2000, 1 semanas.Impactos en fronteras moviles.

14. T.M. Seara, Univ. Texas at Austin, Austin (USA), abr 2000, 2 semanas. Diffusion in Geodesic flows.15. J. Villanueva, Department of Mathematics and Computing Science, Rijksuniversiteit Groningen, Gronin-

gen (Holanda), 2000, 1 semanas. Normal–internal resonances in quasiperiodically forced oscillators.

STAYS YEAR 2001

16. A. Delshams, Centre de Recerca Matematica (CRM), Bellaterra (Espana), 2001–2002, 52 semanas. Atrac-tores no caoticos extranos.

17. Yu. Fedorov, Department of Mathematics, City university of Hong Kong, Kowloon, Hong Kong (China),Abr 2001, 5 semanas. Separation of variables and theta-functional solution for AKNS equation.

18. J.T. Lazaro, Istituto Nazionale per la Fisica della Materia, Florencia (Italia), 2001–02, 54 semanas.Discrete breathers.

19. R. de la Llave, Universitat Politecnica de Catalunya, Barcelona (Espana), jun–jul 2001, 8 semanas. .20. J. Puig, Institut de Mathematiques de Jussieu, Parıs (Francia), 1–31 Oct 2001, 4.5 semanas. Presentacion

y discusion de resultados con L.H. Eliasson.21. P. Roldan, University of Texas at Austin, Texas (EE.UU.), 2001, 16 semanas. Exploracion de la difusion

de Arnold en sistemas Hamiltonianos casi integrables de tipo ‘a priori inestable’, tanto numerica comoanalıticamente.

VISITS YEAR 2001

22. P. Martın, University of Texas at Austin, Austin (USA), 2001, 2 semanas. Invariant objects and transport.23. T.M. Seara, Univ. Texas at Austin, Austin (USA), febrero 2001, 2 semanas. Overcoming the large gaps

poblem.

STAYS YEAR 2002

24. Yu. Fedorov, Department of Mathematics, CIRAM – Universita degli studi di Bologna, Bologna (Italia),May 2002, 5 semanas. Generalized algebraic completely integrable systems.

25. D. Gomez-Ullate, McGill University and Centre de Recherches Mathematiques, Montreal (Canada), sep2002 – dec 2003, 76 semanas. Estancia postdoctoral con N. Kamran and P. Winternitz.

26. R. de la Llave, Universitat Politecnica de Catalunya, Barcelona (Espana), jun-jul 2002, 8 semanas.Overcoming the large gaps poblem.

27. P. Roldan, University of Texas at Austin, Texas (EE.UU.), 2002, 18 semanas. Estudio de objetosgeometricos invariantes y rutas de difusion en sistemas dinamicos Hamiltonianos.

VISITS YEAR 2002

28. Yu. Fedorov, Department of Mathematics, CIRAM – Universita degli studi di Bologna, Bologna (Italia),Sep de 2002, 4 semanas. Integrable billiards with separable potentials.

29. Yu. Fedorov, School of Mathematics, University of Leeds, Leeds (Reino Unido), 2002, 4 semanas. Gen-eralized algebraic completely integrable system.

30. F. Gabern, Institut de Mecanique Celeste et de Calcul des Ephemerides, Observatoire de Paris, Parıs(Francia), 2002, 4 semanas. Estabilidad de los asteroides Troyanos.

31. A. Guillamon, Departamento de Matematica Aplicada II, Universidad de Sevilla, Sevilla (Espana), 2002,0.4 semanas. Period function in dynamical systems.

32. J. Puig, Centre de Mathematiques, Ecole Polytechnique, Palaiseau (Francia), 4–22 Nov 2002, 4 semanas.Presentacion y discusion de resultados con R. Krikorian.

33. T.M. Seara, Univ. Texas at Austin, Austin (USA), abril 2002, 2 semanas. Overcoming the large gapspoblem.

44

STAYS YEAR 2003

34. Yu. Fedorov, Department of Mathematics, North Carolina State university, Ralleigh, NC (EE.UU.),noviembre de 2003, 5 semanas. Discrete nonholonomic systems with right-invariant constraints.

35. F. Gabern, Control and Dynamical Systems, California Institute of Technology, Pasadena (USA), 2003–2004, 66 semanas. Asteroides Binarios.

36. J.R. Pacha, Mathematics Institute, University of Warwick, Coventry (Inglaterra), 1 feb 2003, 52 semanas.On the Poincare’s Second Species Solutions.

37. P. Roldan, University of Texas at Austin, Texas (EE.UU.), 2003-2004, 48 semanas. Calculo de variedadesinvariantes normalmente hiperbolicas.

VISITS YEAR 2003

38. Ch. Pantazi, Centre Emile Borel of the Institut Henri Poincare, Parıs (Francia), 2003, 4 semanas.Dynamical Systems.

39. J. Puig, Dipartimento di Sistemi e Informatica, Universita degli Studi di Firenze, Florencia (Italia), 10–16Mar 2003, 1 semanas. Presentacion y discusion de resultados con R.A. Johnson y R. Fabbri.

40. T.M. Seara, Univ. Texas at Austin, Austin (USA), Mar 2003, 2 semanas. Diffusion in a large gapsproblem.

41. T.M. Seara, Univ. of GATECH, Atlanta (USA), Abr 2003, 2 semanas. Diffusion in a large gaps problem.42. T.M. Seara, IMCCE, CNRS, Paris (Francia), octubre 2003, 1 semanas. Resurgence Theory and Expo-

nentially small phenomena.

STAYS YEAR 2004

43. D. Gomez-Ullate, Dipartimento di Matematica, Universita di Bologna, Bologna (Italia), enero–noviembre2004, 40 semanas. Colaboracion con S. Graffi y M. degli Esposti.

44. J. Puig, Department of Mathematics, California Institute of Technology, Pasadena (USA), Ene 2004,5 semanas. Presentacion y discusion de resultados con B. Simon.

45. P. Roldan, University of Texas at Austin, Texas (EE.UU.), 2004, 16 semanas. Calculo numerico enparalelo de formas normales para sistemas dinamicos Hamiltonianos.

VISITS YEAR 2004

46. P. Acosta-Humanez, Instituto de Matematicas y Ciencias Aplicadas, Lima (Peru), 2004, 2 semanas.Polinomios de Tchebyshev y sus Generalizaciones.

47. P.S. Casas, Oxford Centre for Industrial and Applied Mathematics, Universidad de Oxford, Oxford (ReinoUnido), 2004, 1 semanas. The 49th European Study Group: Mathematics with Industry.

48. J.J. Masdemont, INPE, Instituto Nacional de Pesquisas Espaciais, San Jose dos Campos (Brazil), Nov-Dic2004, 3 semanas. Dynamics of Libration Point Orbits.

49. P. Martın, CNRS, Parıs (Francia), 2004, 1 semanas. Escision de separatrices en la aplicacion de McMillan.50. T.M. Seara, Univ. Texas at Austin, Austin (USA), Mar 2004, 2 semanas. Orbits with unbounded energy

in quasiperiodic geodesis flows.51. T.M. Seara, IMCCE, CNRS, Paris (Francia), octubre 2004, 1 semanas. Resurgence Theory and Expo-

nentially small phenomena.

STAYS YEAR 2005

52. P. Acosta-Humanez, Departamento de Matematicas, Universidad Sergio Arboleda, Bogota (Colombia),Julio y Aug 2005, 8 semanas. Teorıa de Morales–Ramis.

53. E. Canalias, ESOC (European Space Operation Center) of the European Space Agency, Darmstadt(Alemania), 2 May – 12 Aug 2005, 14 semanas. Lissajous orbits around L1 in the Earth–Moon problem:transfer and control strategies.

54. G. Huguet, Department of Mathematics, The Ohio State University, Columbus, Ohio (EE.UU.), 2005,11 semanas. Neurociencia computacional.

45

VISITS YEAR 2005

55. A. Guillamon, Dipartimento di Matematica, Universita degli Studi di Trento, Trento (Italia), 2005,1.3 semanas. Geometric tools for hyperbolicity of limit cycles.

56. G. Huguet, Northeastern Illinois University, Chicago (Illinois, EE.UU.), 2005, 1 semanas. Difusion deArnold.

57. P. Martın, CNRS, Parıs (Francia), 2005, 1 semanas. Escision de separatrices en la aplicacion de McMillan.58. T.M. Seara, IMCCE, CNRS, Paris (Francia), Mar 2005, 1 semanas. Resurgence Theory and Exponentially

small phenomena.59. T.M. Seara, Dpt. Engineering Mathematics, U. Bristol, Bristol (UK), junio 2005, 1 semanas. Visita para

conocer el Master en Engineering Mathematics.60. T.M. Seara, Universidad Sergio Arboleda, Bogota (Colombia), agosto 2005, 1 semanas. Visita para dar

un curso de iniciacion a la resurgencia.61. T.M. Seara, Dpt. Engineering Mathematics, U. Bristol, Bristol (UK), octubre, 1 semanas. Bifurcation

curves in power converters regulation.62. J. Villanueva, Universidad Sergio Arboleda, Bogota (Colombia), 2005, 1 semanas. Teorıa KAM.

46

6.0.4 Group’s visitors

The group keeps close contacts with a large number of researchers of the same area, or relatedareas, from several universities and reseach centers, both national and international. It is of the utmostimportance for the group its ability to finance these contacts. Next we list, in chronological order, thevisits of invited researches of the group during the last years.

VISITORS 2000/2001

1. Alexei Ivanov [SPSU] (St. Petersburg State University).

2. Yuri Fedorov (Moscow State University).

3. David Sauzin [ASD] (Institut de Mecanique Celeste, Paris).

4. Oliver Diaz (Dept. of Math., Univ. of Texas at Austin).

5. Alexei Vasiliev [MSRI] (Space Research Institute, Moscow).

6. Peter Veerman (Dept of Mathematical Sciences, Portland State Univ., Oregon).

7. Martin Golubitsky (Department of Mathematics, Univ. of Houston).

8. Ian Stewart (Mathematics Institute, Univ. of Warwick).

9. Sergey Bolotin [MSU] (Dept. of Mathematics and Mechanics, Moscow State University).

10. Dmitry Treschev [MSU] (Dept. of Mathematics and Mechanics, Moscow State University).

11. Enrico Valdinoci (Univ. of Texas at Austin).

12. Mauricio M. Peixoto (IMPA).

13. Rafael de la Llave (University of Texas at Austin).

14. John Vano (University of Texas at Austin).

15. Julian Barbour (Oxford).

16. Massimiliano Berti (Sissa, Trieste).

17. James Stirling (Dept. Matematica Aplicada I, UPC).

18. Alain Chenciner [ASD] (Astronomie et Systemes Dynamiques, IMCCE, BDL Paris, et Departement deMathematiques, Univ. Paris VII).

19. Masayoshi Sekiguchi (Kisarazu Natl. Col. of Technology, Japan y Dept. Matematica Aplicada i Analisi,UB).

20. Santiago Ibanez [UOV] (Depto. de Matematicas, Univ. de Oviedo).

21. Rafael de la Llave (Dept. of Math. Univ. of Texas at Austin).

22. Freddy Dumortier [LUC] (Limburgs Universitair Centrum).

23. Lorenzo Dıaz (Dept. Matematicas, PUC, Rio de Janeiro).

24. Bernard Malgrange (Univ. de Grenoble I, Institut Fourier).

25. Christian Henriksen (Univ. Paul Sabatier, Toulouse).

26. Serguey Gonchenko [RIAMC] (Dept. Diff. Eq., Univ. Nizhny Novgorod).

27. Ugo Locatelli (Univ. Roma II Tor Vergata).

28. Richard Montgomery (Dept of Math, U. of Calif. at Santa Cruz).

29. Teresa Stuchi (Inst. de Fisica, U. Fed. Rio de Janeiro).

47

30. A. Lopez-Castillo (Centro Universitario FIEO, Brasil).

31. Martijn Van Noort (Dept. of Math. and Comp.Sci. U.of Groningen).

32. Alexander Gofen (Software Deveer Smith-Kettlewell Eye Research Institute, San Francisco).

33. Arturo Olvera (IIMAS, UNAM, Mexico).

34. Dan J. Scheeres (Dept. of Aerospace Engineering, U. of Michigan).

35. Dmitry Treschev [MSU] (Department of Math. and Mech., Moscow State Univ. (Lomonosov University)).

36. George Haller (Department of Mechanical Engineering, MIT).

VISITORS 2002

37. L.M. Lerman [RIAMC] (Univ. de Nizhny Novgorod) from 6 to 20 Abril 2002.

38. Janina Kotus (Warsaw University of Technology).

39. Pascale Roesch (University of Lille).

40. Christian Henriksen (Univ. Paul Sabatier, Toulouse).

41. Serguey Gonchenko [RIAMC] (Dept. Diff. Eq., Univ. Nizhny Novgorod).

42. Alberto Verjovsky (Instituto de Matematicas,UNAM, Cuernavaca).

43. Dmitry Turaev (Weierstrass Institute, Berlin).

44. Patricia Dominguez (Univ. Autonoma de Puebla, Mexico and Dept. de Matematica Aplicada i Analisi,UB).

45. Guillermo Sienra (Depto. de Matematicas, Fac. de Ciencias, UNAM, Mexico and Dept. de MatematicaAplicada i Analisi, UB).

46. Ugo Locatelli (Univ. Roma II Tor Vergata and Univ. de Milano Bicocca).

47. Raphael Krikorian (Centre de Mathematiques, Ecole Polytechnique Palaiseau).

48. Bosco Garcıa-Archilla (Depto. Matematica Aplicada II, ETSIE, Universidad de Sevilla).

49. Joan Sanchez (Dept de Fısica Aplicada, UPC).

50. Luca Biasco (SISSA, Trieste).

51. Stefanella Boatto (IMCCE, Observatoire de Paris and Dept. de Mathematiques, Universite Paris 13).

52. Alexei Vasiliev [MSRI] (Space Research Institute, Moscow) from 16 November to 15 December 2002.

53. Vladimir Gonchenko [RIAMC] (Dept. Diff. Eq., Univ. Nizhny Novgorod.) from 25 November to 10December 2002.

54. Marian Gidea (Northeastern Illinois University) from 16 to 22 December 2002.

VISITORS 2003

55. Joao Carlos Martinho Lopes Dias (Universidad de Cambridge) from 23 February to 1 March 2003.

56. David Sauzin [ASD] (CNRS-IMCCE, Observatoire de Paris) from 17 to 22 de March 2003.

57. Rafael de la Llave (University of Texas at Austin) from 1 June to 31 July 2003.

58. Anna Litvak Hinenzon (University of Warwick) from 1 to 14 June 2003.

59. Joao Carlos Martinho Lopes Dias (Universidad de Cambridge) from 2 to 7 June 2003.

48

60. Katherine Bold (University of Texas at Austin) from 22 to 30 June 2003.

61. Sergey Bolotin [MSU] (Moscow State University and University of Wisconsin) from 22 to 27 June 2003.

62. George Haller (Departament of Mechanical Engineering, MIT) from 22 to 29 June 2003.

63. Kazuyuki Yagasaki (Dept of Mechanical and Systems Engineering, Gifu University) from 2 to 31 July2003.

64. Victor Jose Donnay (Dept of Mathematics. Bryn Mawr College) from 13 to 21 July 2003.

65. Enrico Valdinoci (Universita di Roma Tor Vergata) from 27 July to 1 August 2003.

66. Lev Lerman [RIAMC] (University of Nizhny Novgorod) from 14 to 26 September 2003.

67. Jean-Pierre Marco (Universite de Paris 6) from 13 to 19 October 2003.

68. Rafael Ortega [UGR] (Universidad de Granada) from 23 to 24 October 2003.

69. Laurent Niederman [ASD] (Universite de Paris-Sud (Orsay)) from 26 November to 6 December 2003.

70. Rafael de la Llave (University of Texas at Austin) from 19 to 26 December 2003.

VISITORS 2004

71. Rafael de la Llave (University of Texas at Austin) from 4 to 10 January 2004.

72. Enrico Valdinoci (Universita di Roma Tor Vergata) from 6 to 9 January 2004.

73. Nikola Petrov (University of Michigan) from 27 January to 1 February 2004.

74. Vladimir Gonchenko [RIAMC] (Research Institute for Applied Mathematics and Cybernetics (NizhnyNovgorod)) from 8 February to 3 April 2004.

75. Simonetta Abenda (Universita di Bologna) from 21 to 28 March 2004.

76. David Sauzin [ASD] (CNRS-IMCCE, Observatoire de Paris) from 16 al 24 April 2004.

77. Jean-Pierre Ramis [UPS] (Universite Paul Sabatier) from 19 al 24 May 2004.

78. Luigi Chierchia (Universita degli Studi “Roma Tre”) from 27 June to 4 July 2004.

79. Alain Chenciner [ASD] (Institut de Mecanique Celeste (IMCCE), Paris) from 26 June al 4 July 2004.

80. Sergey Bolotin [MSU] (University of Wisconsin-Madison) from 27 June to 5 July 2004.

81. Diego Moreira (University of Texas at Austin) from 26 June to 5 July 2004.

82. Rafael de la Llave (University of Texas at Austin) from 1 to 31 July 2004.

83. Marian Gidea (Northeastern Illinois University (Chicago)) from 3 to 9 July 2004.

84. Enrico Valdinoci (Universita di Roma Tor Vergata) from 15 to 26 July 2004.

85. Alejandra Gonzalez (University of Texas at Austin) from 23 July al 2 August 2004.

86. Vladimir Gonchenko [RIAMC] (Research Institute for Applied Mathematics and Cybernetics (NizhnyNovgorod)) from 4 September to 17 October 2004.

87. Askold Perelomov (Universidad de Zaragoza) from 25 to 29 October 2004.

88. Jacky Cresson (Universite de Franche-Comte) from 22 to 26 November 2004.

49

VISITORS 2005

89. Marina Gonchenko [RIAMC] (Nizhny Novgorod State University) from 29 January to 13 February 2005.

90. Wang-Sang Koon [CAL] (Caltech) from 19 to 29 March 2005.

91. Alexey Bolsinov (Lomonosov Moscow University) from 18 to 28 April 2005.

92. Simonetta Abenda (CIRAM, Universita di Bologna) from 21 to 30 April 2005.

93. Viktor Enolski (Concordia University (Montreal) / Herriott-Watt University (Edinburgh)) from 5 to 12June 2005.

94. David Terman [OSU] (The Ohio State University) from 19 June to 2 July 2005.

95. John Rinzel [NYU] (Courant Institute, New York University) from 26 June to 2 July 2005.

96. Marian Gidea (Northeastern Illinois University (Chicago)) from 29 June to 5 July 2005.

97. Rafael de la Llave (University of Texas at Austin) from 1 July to 7 August 2005.

98. John Hogan [IOC] (University of Bristol) from 17 to 21 July 2005.

99. Robert Milson [UMG] (Univ. Dalhousie (Canada)) from 25 September to 5 October 2005.

100. Harry Braden [BEE] (University of Edinburgh) from 12 to 16 December 2005.

101. Marco Sabatini (Universita degli Studi di Trento) from 12 to 18 December 2005.

VISITORS 2006

102. Chong-Qing (Univ. de Nanjing) from 9 to 12 January 2006.

103. Rafael de la Llave (University of Texas at Austin) from 9 to 15 January 2006.

104. Pedro Didonato () from 9 January to Summer 2006.

50

6.0.5 National or international groups with a close relationship6.0.5.1 Collaborating groups

[ASD] Jacques Laskar, Alain Chenciner, David Sauzin, Laurent Niederman and others. Astronomie et Sistemes Dy-namiques, CNRS, Paris. Group specialized in frequency analysis, resurgence methods, long time stability ofHamiltonian systems, Solar system, dynamics of accelerating beams, central configurations and nonintegrabilityin celestial mechanics. 4, 12, 16, 18, 20, 47, 48, 49, 56

[BEE] Harry Braden, Chris Eilbeck (in collaboration with Viktor Enol’ski). School of Mathematics, University ofEdimburgh. Group specialized in explicit solutions and geometric properties of algebraically completely integrabledynamical systems. 50

[CAL] J. Marsden, W. Koon, T. Yanao and others in the group of Dynamical Systems and Control of Caltech. Specialistsin dynamics, in a wide sense, and in the use of methods of control theory. 16, 17, 20, 50

[FA] Juan Sanchez, Marta Net, Isabel Mercader et al. Department of Applied Physics, Politechnic university ofCatalonia, Barcelona. Group specialized in instability of convections and rotational flows in dynamics of fluids.13

[GAT] Turgay Uzer, Charlie Jaffe and others. Center for Nonlinear Science, Georgia Institute of Technology, Atlanta.Group with an expertise in the applications of nonlinear dynamics to problems of physical chemistry.

[GRED] Xavier Cabre, Joan Sola-Morales, Jaume Haro, et al. Technical University of Catalonia, Autonoma university ofBarcelona. Group specialized in partial differential equations. 17, 20

[IMPF] Manuel de Leon, David Martın de Diego et al. Institute of Fundamental Mathematics and Physics, Madrid.Group specialized in studying geometrical properties and invariant objects of nonholonomic systems.

[IOC] Enric Fossas, Gerard Olivar (Univ. National of Colombia), Fabiola Angle (Univ. National of Colombia), S. JohnHogan (Univ. Bristol board), Mario di Bernardo (Univ. Bristol) and others, Processes Control group of the IOC(Institut d’Organitzacio i Control de Sistemes Industrials, UPC). This interuniversity group works in the studyof nonregular dynamical systems and its applications to engineering, specially to control theory. 17, 20, 50

[INTE] Yuri Kubyshin, Josep Sempau, Maria Amor Duch and others in the particle accelerators group of the INTE(Institut de Tecniques Energetiques, UPC). Group specialized in study of effects of the dynamics of particle ac-celerating beams, presently it participates in the design of a compact michrotron of circuit (race-track michrotron)in collaboration with several groups of the UPC and the Institute of Nuclear Physics of the University of Moscow.17, 20

[JPL] Martin W. Lo and the others in center JPL of NASA in Pasadena, Orbit Navigation Department. Engineersspecialized in space missions.

[LUC] Freddy Dumortier, Patrick Bonckaert and others. Dynamical Systems of the Limburgs Universitair Centrum.Group specialized in bifurcations of families of vector fields, periodic limit sets, Hilbert 16th problem, singularperturbations, normal forms of fixed points, invariant manifolds. 47

[NYU] John Rinzel, Michael Shelley, Louis Tao and others, Courant Institute, New York University. Specialists incomputational neuroscience and fluid dynamics. Pioneers in the mathematical modelling of physiological processesand in computational techniques of high dimensionality. 15, 20, 50, 56

[RUG] Floris Takens, Henk Broer and others. Dynamical Systems group, Rijksuniversiteit Groningen. Group specializedin normal forms, bifurcation theory, quasiperiodic systems, classification of time series. 17, 20

[MSRI] Anatoly I. Neishtadt, Alexei A. Vasiliev, Nikolai N. Nekhoroshev, Vladislav V. Sidorenko and others. Departmentof Space Geophysics, Moscow Space Research Institute. Specialized group in the theory of adiabatic invariants,modern methods of averages, and KAM theory. 47, 48

[NCSU] Dmitry Zenkov, Anthony Bloch. Department of Mathematics, North Carolina State university. Group specializedin the study of nonholonomic systems.

[MSU] Valery V. Kozlov, Sergey V. Bolotin, Dmitry V. Treschev and others. Department of mechanics and mathematics,Moscow State University. Group specialized in integrability theory and nonintegrabiliy, global variational methodsand theory of perturbations in Hamiltonian systems, averages in systems with slow-fast dynamics, and splittingof separatrices for flows and diffeomorphisms. 12, 18, 47, 48, 49, 56

[ObM] E. Athanassoula, A. Bosman. Observatory of Marseilles. Group specialized in Galactic Dynamics. 16, 20[OSU] David Terman and others. Specialists in mathematical treatment of neuroscience problems: problems of synchro-

nization, travelling waves in the brain, patterns of activity in basal ganglia, subtalmic oscillations, networks ofneurons in the thalamus, singular geometrical perturbations. 16, 20, 50, 56

[RIAMC] Leonid P. Shilnikov, Lev M. Lerman, Sergei V. Gonchenko, Vladimir Gonchenko and others. Department ofDifferential Equations, Research Institute for Applied Math. and Cybernetics. Group specialized in homoclinicphenomena in Hamiltonian and dissipative systems, theory of integrability and nonintegrability, PDE as dynamicalsystems, Hamiltonian systems with slow-fast dynamics. 11, 12, 18, 47, 48, 49, 50

[SPSU] Nikolai Svanidze, Alexei V. Ivanov, Vassili G. Gelfreich and others. Physics Department, St. - Petersburg StateUniversity. Group specialized in the splitting of separatrices of simplectic maps and Hamiltonian systems, expo-nentially small phenomena in theory of perturbations, homoclinic phenomena in the complex domain, positiviyproblems for the entropy of area preserving maps. 47

[UAB] Jaume Llibre, Lluıs Alseda, Armengol Gasull, J.M. Cors, J.M. Mondelo, J. Torregrosa and others. Departmentof Mathematics, Universitat Autonoma de Barcelona. Group specialized in discrete dynamical systems, symbolicdynamics, topologic entropy, ordinary differential equations, celestial mechanics and complex dynamics. 13, 14,15, 16, 18, 19, 20

51

[UAM] Florentino Borondo, Rose M. Benito and others. Department of Chemistry, Universidad Autonoma de Madrid.Group specialized in nonlinear quantum chemistry, multifractal analysis of the phase space structure.

[UB] Carles Simo, Gerard Gomez, Angel Jorba, Ernest Fontich, Alex Haro, Inma Baldoma, Esther Barrabes, ManuelMarcote and others. Departament de Matematica Aplicada i Analisi, Universitat de Barcelona. Group specializedin discrete dynamical systems, symbolic dynamics and complex and holomorphic dynamics, area preserving andsimplectic maps, quasi-periodic systems and reducibility, invariant theory of normal forms and unfoldings, invari-ant manifolds (including their numerical and semi-analytical computation), splitting of separatrices in Hamiltoniansystems with more than one degree of freedom, systems with parabolic fixed points, strange attractors, methodsof detection of chaotic and regular behavior, multiparametric numerical explorations. 5, 12, 13, 14, 15, 16, 18,19, 20, 26, 55

[UCM] Artemio Gonzalez-Lopez, Luis Martinez, Miguel Angel Rodriguez, Federico Finkel. Departamento de MetodosMatematicos de la Fısica, Universidad Complutense. Group specialized in integrable systems in MathematicalPhysics.

[UFI] Russell Johnson and Roberta Fabbri. Dipartimento I gave Sistemi and Informatica. Universta degli Studi diFirenze. Italy. Group specialized in non-autonomous dynamics and applications to Schrodinger operators. 17, 20

[UGR] Rafael Ortega, Juan Campos and others. Departamento de Matematica Aplicada, Universidad de Granada.Group specialized in the forced standard map, classes of homeomorphisms of the plane with simple dynamics andtheir relation with monotonic systems, quasiperiodic and almost-periodic dynamics. 49

[UM] Dario Bambusi, Antonio Giorgilli, Luigi Galgani and others. Dipartimento di Matematica, Universita de Milano.Group specialized in KAM theory, classical perturbation theory, exponential stability, symbolic computations,dynamical systems of infinite dimension (PDE, networks).

[UMG] Niky Kamran, Robert Milson. Department of Mathematics and Statistics, Mc Gill University, Montreal. Groupspecialized in algebraic solutions of the Schrodinger equation in Quantum Mechanics. 16, 20, 50

[UMH] Albert Compte and Maria Victoria Sanchez Vives. Instituto de Neurociencias del CSIC, Universidad MiguelHernandez. AC is specialist in computacional neuroscience and MVS in electrophysiology. The contact with thisgroup allows us to have access to real physiological data and problems of interest in neuroscience. 15, 20

[UOV] Jose Angel Rodrıguez, Santiago Ibanez and others. Departamento de Matematicas, Universidad de Oviedo. Groupspecialized in strange attractors in discrete dynamical systems, symbolic dynamics and topological dynamics. 5,47

[UP6] Jean-Pierre Francoise, Matteo Sommacal and others. Laboratoire J-L Lions, Universite Pierre et Marie Curie,Paris WI. Group specialized in dynamical systems in the plane, applications in circadian rythm, synchronizationand neuroscience. 12, 15, 18, 20

[UPF] Gustavo Deco and others, Universitat Pompeu Fabra. Group specialized in neurodynamic modelling of cogni-tive processes (perception, attention, . . . ). Experts in the computacional treatment of networks of neurons atmesoscalar level, with the use of methods of mean-field. 15, 20

[UPS] Jean-Pierre Ramis and others, Universite Paul Sabatier, Toulouse. Group specialized in integrability and resur-gence methods. 12, 18, 49

[URJC] Andrew Pickering, Pilar Cordoba. Area of Applied Mathematics, University Rey Juan Carlos, Madrid Groupspecialized in Painleve analysis of integrable PDEs and ODEs.

[URLS] Francesco Calogero, Antonio Degasperis, Paolo Santini and Mario Bruschi. Dipartimento di Fisica, Universita diRoma “La Sapienza”. Group specialized in integrable systems, non-linear dynamics and solitons. 12, 18

[UROM] Ugo Locatelli, Alessandra Celletti et al. Mathematics Department, University “Tor Vergata”, Rome. Groupspecialized in celestial mechanics and astronomy dynamics. 16, 20

[UT] Luis Caffarelli and others (Rafael de la Llave appears included in the project). Department of Mathematics,University of Texas at Austin. Group specialized in completely nonlinear PDEs, variational principles, Hamilton-Jacobi equations.

[UW] Robert S. MacKay, Claude Baesens, David Rand, Vassili Gelfreich and others. Mathematics Institute, Universityof Warwick. Group specialized in the break-up of invariant tori, anti-integrable limits, dynamics in space structures(lattices), surfaces of local minimum flow.

6.0.5.2 Other similar groups

[GME] Antonio Elipe, Luis Florıa, Victor Lanchares (Univ. Rioja), Jesus Palacian (Univ. Navarra), Manuel Palacios,Patricia Yanguas (Univ. Navarra) and others. Grupo de Mecanica Espacial, Universidad de Zaragoza. Groupspecialized in dynamical systems, celestial mechanics, normal forms and bifurcation theory, with applications toastrodynamics, atomic physics and molecular dynamics.

[IMPA] Jacob Palis, Marcelo Viana, Welington de Melo and others. Dynamical systems group of the IMPA, Rio deJaneiro. Group specialized in bifurcations, fractional dimensions and strange attractors, conservative dynamics,dynamics and holomorphic foliations, maps of the interval, differentiable ergodic theory. 5

[US] Emilio Freire, Enrique Ponce and others. Departamento de Matematica Aplicada II, Universidad de Sevilla. Groupspecialized in normal forms, local bifurcations and continuation of periodic orbits in dissipative and conservativesystems, modelled and control of dynamical systems in engineering, with emphasis in electronic and mechanicaldevices.

[UVA] Rafael Obaya, Sylvia Novo and others. Departamento de Matematica Aplicada a la Engenierıa, Universidad deValladolid. Group specialized in ergodic theory, topological dynamics and monotone systems.

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6.2 PUBLIC AND PRIVATE GRANTED PROJECTS AND CONTRACTS OF THERESEARCH GROUPIndicate the project and contract grants during the last 5 years (2004-2008) (national, regional or international)Include the grants for projects under evaluation

R & D projects and contracts of the members of the UPC Group (2004-2008)

Title of the project or contractRelationship

with thisproposal (1)

PrincipalInvestigator

Budget

EURO

Fundingagency and

projectereference

Projectperiod

(2)

Estudio global de sistemasdinamicos. Aplicaciones.

0 C. Simo 19 000 000 pts. DGICYTPB94–0215

1995–2000(C)

Ajut per a Grups de recercaconsolidats 1998

1 C. Simo 3 900 000 pts. CIRIT1998SGR–00041

1998–2000(C)

First Guess Module forLTOOL

2 G.Gomez[UB],J. Masdemont[UPC]

10 000 USD NASA-JPLContract NAS7-1407

1999–2000(C)

Formation Flight near Libra-tion Point Study

2 Martin W. Lo 8 000 USD NASA-JPL 2000(C)

Hyperbolicity and diffusion inHamiltonian systems

2 A. Delshams 57 000 Euros INTAS97-0771

1999–2001(C)

Computational and Analyti-cal Dyn. Syst. Techniques forthe Study of Global Dynamicsin Theoretical Chemistry

1 Stephen R.Wiggins[Caltech]

18 000 USD Nat. Science Founda-tion(NSF INT-9910336)

1999–2001(C)

Non-linear evolution eq. anddynamical systems

2 M. Boiti[Univ. Lecce]

60 000 Euros INTAS 2000–2001(C)

Transiciones entre objetos in-variantes de sist. dinamicos

2 A. Delshams,R. de la Llave

1 200 000 pts. Programa CatedraFBBV 2000

2001(C)

Transporte y objetosinvariantes en sistemas dina-micos y aplicaciones

1 A. Delshams,R. de la Llave

14 800 USD Comision Espana-USACoop. Cientıfica y Tec-nol. BOE 18-05-2000

2000–2002(C)

Ajut per a Grups de recercaconsolidats 2000

1 C. Simo 5 950 000 pts. CIRIT2000SGR–00027

2000–2002(C)

La medida del caos y la teorıade la resurgencia de Ecalle

1 A. Delshams 200 000 pts. Serv. pour Sci. et Tech.,Emb. Franc. en Espana

2001–2002(C)

Smooth Varieties and Charac-teristic Classes with Applica-tions to Math. Physics

1 V. Buchstaber[Lomonosov]

4 250 Euros Russian Foundation ofBasic Researches, ref.RFBS 02-01-00659

2002(C)

Personal Calificado soporte ala lınea Sistemes Dinamics

2 A. Delshams 6 000 000 pts. Com. Univ. Recerca yUPC, ref. PQS/031

2000–2009(C)

Estudio global del espacio defases de S.D. en dimen. finita

0 A. Delshams 4 180 000 pts. DGICYTBFM2000-0805-C02

2000–2003(C)

Estabilidad y difusion enproblemas de Astronomıa

1 Angel Jorba[UB]

21 246 Euros DGICYTBFM2000-0623

2000–2003(C)

Chaotic motion and stabilityin (near) conservative systems

2 A. Delshams 120 000 Euros INTAS2000-221

2001–2003(C)

Accion Especial.International Conference onLibration Point Orbits

2 Josep J.Masdemont

6 000 Euros MCyT(AYA2001-4453-E)

2002–2003(C)

Ajut per a Grups de recercaconsolidats 2001

1 C. Simo 9 000 000 pts. CIRIT2001SGR–70

2001–2004(C)

Dinamica no lineal en dim.baja y atractores extranos

2 Lluıs Alseda[UAB]

6 000 Euros MCyTBFM2001-5237-E

2002–2004(C)

Dinamica no lineal endimensio baixa i atractorsestranys

1 Ll. Alseda,A. Delshams[UAB / UPC]

5 400 Euros CIRIT, Xarxa temati-ca n◦2002/XT/00094

2002–2004(C)

(1) Write 0, 1, 2 or 3 according to: 0 = Similar project; 1 = Very related; 2 = Low related; 3 = Unrelated.(2) Write C or S if the project has been funded or it is under evaluation, respectively.

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R & D projects and contracts of the members of the UPC Group (2000-2005)

Title of the project or contractRelationship

with thisproposal (1)

PrincipalInvestigator

Budget

EURO

Fundingagency and

projectereference

Projectperiod

(2)

Herramienta analıtica y num.para el control distribuido desatelites en formacion

2 A. Caramagno,G. Gomez,J. Masdemont

81 900 Euros PROFITDICOFF-DMS-PRO

2002–2004(C)

Geometrical study of differen-tial equations

2 N. Kamran[Mc Gill Uni-versity]

25 530 Euros Natural Sciences andEng. Research Councilof Canada (NSERC)

2002–2004(C)

Summer Workshop onAdvanced Topics in Astrody-namics

2 G.Gomez[UB],M. Lo [JPL],J. Masdemont[UPC]

20 000 Euros NASA-JPLJPL-1263386013/04

2004(C)

Analysis for Dynamical Sys-tems Tools and Applicationsfor Mission Design

2 G.Gomez[UB],J. Masdemont[UPC]

31 000 Euros NASA-JPL 2004(C)

Assessment of Mission DesignIncluding Utilisation of Libra-tion Points and Weak Stabil-ity Boundaries

2 Josep J.Masdemont

15 000 Euros Agencia EspacialEuropeaARIADNA 03/4103n◦18142/04/NL/MV

2004(C)

Modelos cuasiexactamente so-lubles en Fısica Cuantica

2 A. Gonzalez[U. Complut.]

70 350 Euros DGUIBFM2002-02646

2002–2005(C)

Grup de Sistemes Dinamics iTeoria Qualitativa de la UAB.Suport a grups de recerca dequalitat

2 Jaume Llibre[UAB]

51 687 Euros CONACIT2001SGR-00173

2002–2005(C)

Estudio cualitativo de los Sis-temas Dinamicos con enfasisen las bifurcaciones

1 Jaume Llibre[UAB]

252 840 Euros DGESBFM2002-04236-C02-02

2002–2005(C)

Contract for services aboutJIMO software support andconsultation

2 G.Gomez[UB],J. Masdemont[UPC]

6 000 USD NASA-JPLJPL-OR n◦1254206

2003–2005(C)

Caos en sistemas dinamicos:su relacion con el fenomeno dela difusion y la teorıa de laresurgencia de Ecalle

1 Tere M.-Seara 10 200 Euros Accion integradaHF2002-0058

2003–2005(C)

Dinamica, Atractores y Nolin-ealidad: Caos y Estabilidad

1 Ll. Alseda,A. Delshams[UAB / UPC]

18 000 Euros Red tematicaBFM2002-12129-E

2004–2005(C)

Accion Especial. SeminarioInternacional en temas avan-zados en Astrodinamica

2 Josep J.Masdemont

8 000 Euros MCyTESP2002-12362-E

2004–2005(C)

Objetos invariantes en sist.dinamicos: conexiones, evolu-cion respecto de parametros yaplicaciones (OICEPA)

0 A. Delshams 197 920 Euros MCyT-FEDERBFM 2003-9504-C02-02

2003–2006(C)

Dinamica Recurrente y Apli-caciones

1 A. Jorba [UB] 97 920 Euros MCyTBFM2003-07 521-C02-01

2003–2006(C)

Development of a LibrationOrbit Design Tool

2 Gerard Gomez[UB],Miguel Bello[DEIMOS SL]

180 000 Euros Agencia Espacial Eu-ropea. ESA Contractn◦18426/04/D/HK

2004–2006(C)

Dinamica no lineal endimensio baixa i atractorsestranys

1 Ll. Alseda,A. Delshams[UAB / UPC]

8 400 Euros CIRIT, Xarxa temati-ca n◦2004/XT/00053

2005–2006(C)

Dinamica, Atractores y Nolin-ealidad: Caos y Estabilidad

1 Ll. Alseda,A. Delshams[UAB / UPC]

12 000 Euros Red tematica n◦

MTM2005-23973-E2006(C)

Grup de recerca consolidat2005

1 A. Delshams CIRITn◦2005SGR-986

2005–2008(C)

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7. TRAINING CAPACITY OF THE PROJECT AND THE GROUP(In the case of Coordinated Projects this issue must be filled by each partner)

This title must be filled only in case of a positive answer to the corresponding question in the application form.Justify that the group is able to receive fellow students (from the Suprograma de Formacion de Investigadores)associated to this project and describe the training capacity of the group. In the case of coordinated projects,each subproject requesting a FPI fellowship must fill this issue.Note that all necessary personnel costs should be included in the total budget requested. The availablenumber of FPI fellowships is limited, and they will be granted to selected projects as a function of their finalqualification and the training capacity of the groups.

Educational capability of the UPC project

In general, the UPC group, as we have already remarked, has now a great educational capabilityspecially due to the maturity of its researchers (2/3 of the group are senior Ph.D.’s between 30 and 50years old), who are now experts in some subjects which have the “trademark” of the dynamical systems’group of Barcelona. Therefore, the group is now in an excellent position to educate young researchers inany of the main topics of this project.

On the other hand, several graduate students have recently joined the group. They can benefit fromthis knowledge and pursue their doctoral thesis thanks to different kinds of scholarships.

It is worth to emphasize that in the last four years, 7 members of the group have defended theirdoctoral theses (J.T. Lazaro, J.R. Pacha, P. Casas, F. Gabern, D. Gomez-Ullate, J. Puig, Ch. Pantazi)and 6 doctoral theses have been directed by members of the group. Specifically: A. Delshams has co-directed, together with Ana Sastre (UPC), the thesis defended by Maria Graciela Benzal on 25-06-2003;A. Delshams has directed the thesis defended by J.T. Lazaro on 23-10-2003; M. Olle and J. Villanuevahave co-directed to thesis defended by J.R. Pacha on 21-10-2002; J. Villanueva has codirected, togetherwith A. Jorba [UB] the thesis defended by Alejandra Gonzalez on 16-07-2002; and Y. Fedorov has directedthe thesis defended by Alexey Tsygvintsev on 19-6-2001, and the thesis defended by Alexander Kuleshovon 1-6-2001. In addition, it is expected that C. Olive and Sergi Simon will defend their theses on March2006; their directors are T.M. Seara respectively J.J. Morales.

The increase of students who have different graduate scholarships (FPU, FPI, FI and also foreignstudents with scholarships granted by their home government) causes that there are currently 6 membersof the group who are directing 9 theses that will be defended in the next 4 years. Specifically: T.M.Seara is directing the thesis of the student C. Olive; A. Delshams and R. de la Llave are codirecting tothesis of P. Roldan; A. Delshams and A. Guillamon are codirecting the thesis of G. Huguet; J. Villanuevais directing to thesis of A. Luque; J. Masdemont is codirecting, together with Gerard Gomez [UB] thethesis of M. Marcote [UB] and Elisa Maria Alessi [UB], and the theses of E. Canalias, M. Romero,L. Garcıa and Luis Ortiz. Moreover, in the last year four new students have joined the group: J.M.Benita (Mexico), who has started his thesis under the supervision of A. Guillamon; P. Acosta-Humanez(Colombia) and D. Blazquez (Univ. of Barcelona), who have started their theses under the supervision ofJ.J. Morales; Marina Gonchenko (Russia) who has started her thesis with A. Delshams; and O. Larreal(Venezuela) and M. Guardia, who have started their theses under the supervision of T.M. Seara, all ofthem by obtaining competitive scholarships from the MEC, the DURSI in Catalunya, or other equivalentinstitutions in Mexico and Venezuela. In addition to directing doctoral theses, J. Masdemont has alsodirected to “tesina” research projects of Lorenzo Arona (Italy) and Pedro di Donato (Brazil).

The group has very close ties to the graduate program in Applied Mathematics of the UniversitatPolitecnica de Catalunya. This program has been awarded with the excellence award “Mencion decalidad” (MCD2003-00136) of the Ministry of Education and Science. On the one hand, the relation of thegroup with the graduate program comes from the fact that 6 researchers of the group are teaching in thisprogram the courses: “Algebraic methods in dynamical systems” (J.J. Morales), “Asymptotic methods indynamical systems” (T.M. Seara), “Simulation methods (D. Gomez-Ullate, A. Guillamon), “Qualitativeand quantitative methods in dynamical systems” (A. Delshams, P. Gutierrez) and “Hamiltonian systemsand celestial mechanics” (A. Delshams).

On the other hand, the current coordinator of the graduate program (T.M. Seara) is a member ofthe group. In addition, within the Applied Mathematics program, and thanks to travel grants from theMinistry, the group of dynamical systems has been able to contract each year several external professors,experts in very recent topics, who have participated in some courses of the program. These courses have

55

been organized in the form of Thematic programmes to which a large number of students have attended.Specifically:

Academic year 2001/2002 (ref: MOVI01200) Professors David Sauzin (Institut de Celestial Meca-nique, CNRS), Sergey Bolotin [MSU], Dmitry Treschev [MSU] and Rafael Ortega (U. Granada), taughtthe courses “Asymptotic Methods in Dynamical Systems”, “Qualitative and quantitative Methods inDynamical Systems ” and “Hamiltonian systems and cellestial mechanics”.

Academic year 2002/2003 (ref: DCT2002-00074) Professors Rafael de la Llave (U. Texas) and GeorgeHaller (MIT) taught the courses “Asymptotic Methods in Dynamical Systems” and “Qualitative andquantitative Methods in Dynamical Systems”.

Academic year 2003/2004 (ref: DCT2003-00074) Professors Luigi Chierchia (U. degli Studi “RomeTre”) and Alain Chenciner [ASD] taught the courses “Asymptotic Methods in Dynamical Systems” and“Hamiltonian systems and cellestial mechanics”.

Academic year 2004/2005 (ref: DCT2004-00078) Professors John Rinzel [NYU], Michael Shelley[NYU] and David Terman [OSU] taught the courses “Simulation Methods” and “Hamiltonians systemsand cellestial mechanics”.

These thematic programmes, which will be held again this year, contemplate the attendance of stu-dents from other Spanish and foreign universities who, in case of being able to obtain scholarships, couldthen start their doctoral thesis directed by members of our group. More information on these thematicprogrammes can be found in http://www.ma1.upc.edu/recerca/pestanyarecerca.html #seminaris.

Finally, it is remarkable that the seminar “Sistemes Dinamics UB-UPC” (http://www.maia.ub.es/ssd.html) has been held uninterruptedly since 1978, with one or more talks every Wednesday afternoon.It is useful to attract new researchers, to learn or get acquainted with other research topics in dynamicalsystems as well as to present new results in public.

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