Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Regularity of entropy on non compact negatively curved manifolds

Barbara Schapira talk

Speaker invited by: Prof. Dr. Corinna Ulcigrai

**Date:** 18.02.19 **Time:** 14.00 - 15.00 **Room:** ETH HG G 43

In this work, we proved that the entropy of the geodesic flow of non compact manifolds varies in a C1-way along a C1-variation of metrics, under an assumption, called Strong positive recurrence, which is satisfied on a wide class of non compact manifolds. It generalizes an old result of Katok-Knieper-Weiss in the compact case. This assumption means that a certain entropy at infinity is strictly smaller than the topological entropy. I will explain the relevant concepts and strategy of the proof. Joint work with Samuel Tapie.