EVENT DETAILS AND ABSTRACT

Title: Uniqueness of the measure of maximal entropy for the standard map
Speaker: Davi Obata
Speaker Info: U. Chicago
Brief Description: Part of Midwest Dynamics Conference
Special Note: Part of Midwest Dynamics Conference
Abstract:

The standard family (or Taylor-Chirikov standard family) is a famous example of a family of dynamical systems having a “simple expression” but with complicated dynamics. A famous conjecture by Sinai states that for large parameters the standard map has positive entropy for the Lebesgue measure. In this talk, I will discuss the proof of the uniqueness of the measure of maximal entropy (m.m.e.) of the standard map for sufficiently large parameters. If time permits, I will also explain some properties for this mme, such as equidistribution of “sufficiently hyperbolic” periodic points and estimates on the dimension of this measure.