MEASURES OF MAXIMAL ENTROPY THAT ARE SRB

讲座题目：MEASURES OF MAXIMAL ENTROPY THAT ARE SRB
讲座时间 Datetime: 2025年 5 月 22 日，周四，10：30-12：00
地点 Venue: 海琴2号楼A457
主持人 Host：Sergio Augusto Romana Ibarra副教授
报告人 Speaker: Raul Mario Ures de la Madrid 教授
单位 Affiliation: 南方科技大学
报告摘要 Abstract:
Abstract: How often does it occur that the measure of maximal entropy
of a system is an SRB measure? We will talk about this question for C1+α  partially hyperbolic diffeomorphisms isotopic to Anosov (DA-diffeomorphisms) on T3, and establish a rigidity result: the measure of maximal entropy is an SRB measure if and only if the sum of its positive Lyapunov exponents coincides with that of the linear Anosov map A on all periodic orbits of the support of the measure. 
We will also show that a volume-preserving C1+α DA diffeomorphism on
T3 is Anosov if all Lyapunov exponents coincide almost everywhere with
those of the linear Anosov in its isotopy class. Consequently, a smooth DA diffeomorphism is smoothly conjugated to its linear part if and only if all Lyapunov exponents coincide almost everywhere with those of its linear part. 
This talk is based in a joint work with Fernando Micena, Ryo Moore, and Jana R. Hertz. 
报告人简介：
Professor Raul has several relevant publications in Journal as "Duke Mathematical Journal", "Inventiones Mathematicae" , "Acta Mathematica" , "Communications in Mathematical Physics" . Moreover, he is a Simons Associate at ICTP, Trieste - Italy and 1000 Thousand Talent Program 2017 (China).