【03-26】Chaos on the surface-Jérôme BUZZI

Title: Chaos on the surface

Speaker: Jérôme BUZZI，Centre national de la recherche scientifique, CNRS & Université Paris-Saclay

Time: 2025-03-26, 16: 00-17: 00

Place：Room 5406, No. 5 Teaching Building, USTC

Abstract:

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.

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