29 May 2002, 14.15-16.00, Lille Auditorium.

Yakov Pesin (Penn State University, USA) "Chaotic traveling waves in coupled map lattices of unbounded media".

I will consider coupled map lattices (CML) of unbounded media, i.e., time and space discretize versions of some  well-known evolution partial differential equations (including reaction-diffusion equation, Kuramoto-Sivashinsky, Swift-Hohenberg, and Ginzburg-Landau equations). Following Kaneko CML are viewed also as phenomenological models of the medium. I present the dynamical system approach to study the global behavior of solutions of CML. In particular, I discuss spatio-temporal chaos associated with the set of traveling wave solutions of CML as well as describe the dynamics of the  evolution operator on this set. Several examples will be given to illustrate the appearance of  Smale horseshoes and the  presence of the dynamics of Morse-Smale type.