Uniqueness of the measure of maximal entropy for geodesic flows on coarse hyperbolic manifolds without conjugate points

TL;DR

This paper proves the uniqueness of the measure of maximal entropy for geodesic flows on certain hyperbolic manifolds without conjugate points, extending previous results to broader geometric conditions.

Contribution

It establishes the uniqueness of the measure of maximal entropy for geodesic flows on manifolds with Gromov hyperbolic and residually finite fundamental groups, without requiring negative curvature.

Findings

Uniqueness of the measure of maximal entropy under specified conditions

Generalization of previous results to broader geometric settings

Applicable to manifolds without conjugate points and divergence properties

Abstract

In this article we study geodesic flows on closed Riemannian manifolds without conjugate points and divergence property of geodesic rays. If the fundamental group is Gromov hyperbolic and residually finite we prove, under appropriate assumptions on the expansive set, that the geodesic flow has a unique measure of maximal entropy. This generalizes corresponding results of Climenhaga, Knieper and War proved under the stronger assumption of the existence of a background metric of negative sectional curvature.