On the geodesic flow on CAT(0) spaces

TL;DR

This paper proves that the geodesic flow on certain CAT(0) spaces is topologically mixing without requiring Bowen-Margulis measure finiteness, and provides examples of spaces lacking finite Bowen-Margulis measure.

Contribution

It establishes topological mixing of geodesic flow under new assumptions and removes the need for Bowen-Margulis measure finiteness in this context.

Findings

Geodesic flow is topologically mixing on certain CAT(0) spaces.

Finiteness of Bowen-Margulis measure is not necessary for mixing.

Examples of CAT(0) spaces without finite Bowen-Margulis measure.

Abstract

Under certain assumptions on CAT(0) spaces, we show that the geodesic flow is topologically mixing. In particular, the Bowen-Margulis' measure finiteness assumption used in recent work of Ricks is removed. We also construct examples of CAT(0) spaces which do not admit finite Bowen-Margulis measure.