In this last lecture I will introduce and study the notion of topological entropy associated with a dynamical system, and exhibit its connection with the Kolmogorov-Sinai entropy.
I will then focus on a specific type of system, namely differentiable systems with a hyperbolic behaviour (at least on part of phase space). We will see how hyperbolicity implies complexity (in the form of a positive topological entropy).

(Cour organisé en collaboration avec l’Ecole Doctorale de Physique de la Région Parisienne – ED 107)

IPhT