Marta Canadell

ICERM Institute Postdoc 2015-2016

ICERM Semester Program on "Dimension and Dynamics"February 1 - May 6, 2016

Sant Feliu de Guíxols, Girona Barcelona

Dynamical Systems

The long term behavior ofa dynamical system

is organized by its invariant objects

the SKELETONof the system

FIXED POINTS, PERIODIC ORBITS, INVARIANT MANIFOLDS...

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The invariant objects that are ROBUST, i.e. persistent underperturbations of the system, are very important. These objects areendowed with hyperbolicity properties.

Computation of Normally HyperbolicInvariant ManifoldsInvariant ManifoldWe say that the manifold parameterizedby K is F -invariant with internaldynamics f if K and f meet theinvariance equation:

F ◦ K = K ◦ f

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The setting: general idea? Algorithmic treatment of invariant equation

? By using a Newton-like method the linearizedequations have a geometric structure:

X improved speed: Fast methodX improved storage requirementX improved stability

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PhD Advisor: Àlex HaroDept. Matemàtica Aplicada i Anàlisi, Universitat de Barcelona

Dynamical Systems - Invariant Manifolds

with Rafael de la LlaveYear 2014-2015

with Roman Grigorievat Center for Nonlinear ScienceSummer 2015

This 2015-2016 year:

at 10th floor, office 123

Thank you! - Moltes gràcies!