Equilibrium measures of manifolds without conjugate points having visibility covering

TL;DR

This paper investigates equilibrium measures for geodesic flows on certain manifolds, establishing uniqueness and ergodic properties under specific geometric conditions and potential functions.

Contribution

It proves the weak pressure gap for Bowen potentials on manifolds with visibility universal coverings and studies their ergodic properties.

Findings

Uniqueness of equilibrium measures under specified conditions

Ergodic properties such as K-mixing and Gibbs property established

Weak pressure gap proven for certain potentials

Abstract

In this paper we study the equilibrium measures of geodesic flows of closed manifolds without conjugate points which have a visibility universal covering. Specifically, the uniqueness problem for Bowen potentials which are constants on some sets--intersection of horospheres-- and satisfy a weak pressure gap. Moreover, we study some ergodic properties of these measures such as the K-mixing property, weighted equidistribution of closed geodesics, the Gibbs property, large deviations and the entropy density of ergodic measures. Assuming, furthermore continuity of Green bundles, existence of a hyperbolic closed geodesic and a Gromov hyperbolic universal covering we prove that the above potentials always satisfy the weak pressure gap.