题目: Chaos on the surface

报告人：Jérôme BUZZI，Centre national de la recherche scientifique（法国国家科研中心）

时间：3月26日，16：00-17：00

地点：东区第五教学楼5406

摘要：It was noticed by Newhouse that surface diffeomorphisms in positive entropy share some of the chaotic flavor of the uniform hyperbolicity of Anosov-Smale.

In a joint project with Sylvain CROVISIER and Omri SARIG, we have indeed generalized many properties of the Anosov-Smale dynamics to arbitrary smooth surface diffeomorphisms with positive entropy: finite multiplicity of the measures maximizing the entropy, exponential mixing, almost sure invariance principle, and many other statistical properties typical of a spectral gap. I will try to explain how this is proved by introducing a general notion of strong positive recurrence for diffeomorphisms.