Seminar 5.31.18 Kao

Title: Unique Equilibrium States for Geodesic Flows on Surfaces without Focal Points

SpeakerNyima Kao (University of Chicago)

Abstract: It is well-known that for compact uniformly hyperbolic systems Hölder potentials have unique equilibrium states. However, it is much less known for non-uniformly hyperbolic systems. In his seminal work, Knieper proved the uniqueness of the measure of maximal entropy for the geodesic flow on compact rank 1 non-positively curved manifolds. A recent breakthrough made by Burns, Climenhaga, Fisher, and Thompson which extended Knieper’s result and showed the uniqueness of the equilibrium states for a large class of non-zero potentials. This class includes scalar multiples of the geometric potential and Hölder potentials without carrying full pressure on the singular set. In this talk, I will discuss a further generalization of these uniqueness results, following the scheme of Burns-Climenhaga-Fisher-Thompson, to equilibrium states for the same class of potentials over geodesic flows on compact rank 1 surfaces without focal points. This work is an MRC project joint with Dong Chen, Kiho Park, Matthew Smith, and Régis Varão.