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.