Title: Uniqueness of the measure of maximal entropy for the standard map
Abstract: Understanding the dynamics of a nonlinear system can be a very hard task, even for systems having a simple expression. A good example of such a system is the (Taylor-Chirikov) standard map. Sinai conjectured that the standard map has positive metric entropy for large parameters (i.e., it has a set of positive Lebesgue measure having non-zero Lyapunov exponents). The dynamics of the standard map is far from being well understood. In this talk, I will discuss some progress in the understanding of the dynamics of the standard map.