A note on the density of periodic orbits of Anosov geodesic flow in manifolds of finite volume

TL;DR

This paper proves that in finite volume manifolds with Anosov geodesic flow, periodic orbits are dense, extending to non-compact conservative Anosov flows, highlighting the ubiquity of periodic orbits in such dynamical systems.

Contribution

It establishes the density of periodic orbits for Anosov geodesic flows on finite volume manifolds, including non-compact cases, which was previously not fully understood.

Findings

Periodic orbits are dense in finite volume manifolds with Anosov geodesic flow.

The density result extends to conservative Anosov flows in non-compact settings.

The work generalizes known results to broader classes of manifolds and flows.

Abstract

In this paper, we prove that manifolds of finite volume with Anosov geodesic flow have dense periodic orbits. The same result works for conservative Anosov flows in non-compact cases.