Stochastic Properties for Measures of Maximal Entropy for Smooth Surface Diffeomorphisms
Talk by Prof. Dr. Omri Sarig
Speaker invited by: Prof. Dr. Corinna Ulcigrai
Date: 20.05.26 Time: 13.30 - 14.30 Room: ETH HG G 19.1
Suppose \(f\) is a general infinitely differentiable topologically mixing surface diffeomorphism with positive topological entropy.
We show that the measure of maximal entropy is Bernoulli, and that all smooth observables exhibit exponential decay of correlations, the strong almost sure invariance principle, and (consequently) the central limit theorem and the law of the iterated logarithm.
The proof, joint with Crovisier and Buzzi, is based on a new dynamical property called "strong positive recurrence," which guarantees the existence of a symbolic model with spectral gap for the associated transfer operator.
(Joint with S. Crovisier & J. Buzzi)