报告人：Jerome Buzzi，CNRS研究员，法国巴黎萨克雷大学

地点：5506

时间：4月24日（周五） 10:00-12:00

题目：Measures maximizing the entropy for discretized Anosov flows 

摘要：

We study ergodic measures maximizing the Kolmogorov-Sinai entropy (MME for short). Existence is known under rather general conditions. Understanding multiplicity and ergodic properties is much more demanding.

Topologically transitive uniformly hyperbolic diffeomorphisms have a unique MME. However such systems are not generic and it is an important goal to understand how this generalizes. In this talk we consider « Discretized Anosov Flows », this is an open class of diffeomorphisms including time-one maps of Anosov flows. 

Assuming an open irreducibility condition, we prove the following dichotomy:

      - either there is a unique MME and it has a zero central exponent;

      - or there are exactly two MMEs and they have nonzero central exponents of opposite sign, are isomorphic to Bernoulli, and have exponential mixing.

Moreover, the second case is open and dense.

This is a work in progress with Sylvain Crovisier, Mauricio Poletti, Ali Tahzibi.