Geodesic flows modeled by expansive flows

TL;DR

This paper demonstrates that geodesic flows on certain compact surfaces can be modeled by expansive flows, leading to insights about their entropy and measure properties.

Contribution

It introduces a semi-conjugate expansive flow model for geodesic flows on surfaces without focal points, preserving time-parametrization.

Findings

Geodesic flow is semi-conjugate to an expansive flow with local product structure.

The geodesic flow has a unique measure of maximal entropy.

Abstract

Given a smooth compact surface without focal points and of higher genus, it is shown that its geodesic flow is semi-conjugate to a continuous expansive flow with a local product structure such that the semi-conjugation preserves time-parametrization. It is concluded that the geodesic flow has a unique measure of maximal entropy.