Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Measures of maximal entropy for smooth surface diffeomorphisms (e-seminar)

Talk by Prof. Dr. Omri Sarig

**Date:** 07.12.20 **Time:** 15.00 - 16.15 **Room:** Y27H28

Thirty years ago, Sheldon Newhouse proved that every C^\infty diffeomorphism on a compact manifold has at least one measure of maximal entropy. I will explain the proof of the following result (joint with J. Buzzi and S. Crovisier): If the diffeomorphism has positive topological entropy, and if the dimension of the manifold is equal to two, then there are at most finitely many different ergodic measures of maximal entropy, and in the topologically transitive case -- exactly one (joint work with J. Buzzi and S. Crovisier).