Geodesic flows of compact higher genus surfaces without conjugate points have expansive factors

TL;DR

This paper proves that geodesic flows on compact higher genus surfaces without conjugate points are semi-conjugate to expansive flows, leading to unique measures of maximal entropy and providing an alternative proof of a known theorem.

Contribution

It establishes a semi-conjugacy to an expansive flow for geodesic flows on such surfaces, revealing new dynamical properties and confirming uniqueness of maximal entropy measures.

Findings

Existence of a semi-conjugacy to an expansive flow

Flow is topologically mixing with local product structure

Uniqueness of the measure of maximal entropy

Abstract

In this paper we show that a geodesic flow of a compact surface without conjugate points of genus greater than one is time-preserving semi-conjugate to a continuous expansive flow which is topologically mixing and has a local product structure. As an application we show that the geodesic flow of a compact surface without conjugate points of genus greater than one has a unique measure of maximal entropy. This gives an alternative proof of Climenhaga-Knieper-War Theorem.