Speaker：Dong Chen（The Pennsylvania State University，US）

Time：2022-06-01, 20:30

Location：Tencent Meeting ID：455502384（No Pwd）

Abstract:

The geodesic flow over a closed negatively curved manifold is Anosov, thus any Hölder potential has a unique equilibrium state. However, it is much less known for non-uniformly hyperbolic geodesic flows. Knieper proved the uniqueness of the measure of maximal entropy for the geodesic flow on compact rank 1 non-positively curved manifolds, and it was extended by Burns, Climenhaga, Fisher, and Thompson to the uniqueness of the equilibrium states for a large class of non-zero potentials with pressure gap. In this talk, I will discuss related uniqueness results for geodesic flows without focal points, and some recent results regarding potentials with pressure gap. This work is joint with Lien-Yung Kao and Kiho Park.