MERCREDI 08 JUILLET 2009
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Roberto Livi
Center for the Study of Complex Dynamics
(CSDC), Department of Physics, University of Florence, Italie

Title: How to measure covariant Lyapunov vectors (and exponents)

Abstract: The seminar aims at a pedagogical presentation of the mathematical
tools that one has to deal with for characterizing determinsitic
chaos in flows on differentiable manifolds. The ergodic multiplicative
theorem by Oseledec allows to identify all the necessary ingredients
to cope with this goal. On the other hand, the transltion of the
rigorously defined procedure into effective algorithms is far from
trivial. In particular, we shall discuss how to measure the covariant
Lyapunov vectors, that allow a complete local reconstruction of the
stable and unstable manifolds in phase space, thus providing a
representation of the so-called "Oseledec splitting". We shall conclude
with some comments on possible applications.