22 May | 11h00min | Davi Obata (Univ. Cergy-Pontoise, France)
Title: Uniqueness of the measure of maximal entropy for the standard map (video)
The standard family (or Taylor-Chirikov standard family) is an example of a family of dynamical systems having simple expressions but with complicated dynamics. A famous conjecture of Sinai is that for large parameter the standard map has positive entropy for the Lebesgue measure.
In this seminar, I will talk about the uniqueness of the measure of maximal entropy (m.m.e.) of the standard map for sufficiently large parameters. There are several other properties obtained for this m.m.e. We obtain that it is Bernoulli; the periodic points whose Lyapunov exponents are bounded away from zero equidistribute with respect to the m.m.e. We also obtain estimates of the Hausdorff dimension of the measure and of its support.