Ruelle's inequality and Pesin's formula for Anosov geodesic flows in non-compact manifolds

TL;DR

This paper extends Ruelle's inequality and Pesin's formula to Anosov geodesic flows on non-compact manifolds under certain curvature conditions, advancing the understanding of dynamical systems in geometric contexts.

Contribution

It proves Ruelle's inequality and Pesin's formula for Anosov geodesic flows on non-compact manifolds with specific curvature assumptions.

Findings

Ruelle's inequality holds for non-compact manifolds with Anosov geodesic flow.

Pesin's formula is established for finite volume non-compact manifolds.

The results depend on curvature conditions and extend classical ergodic theory to broader geometric settings.

Abstract

In this paper, we prove Ruelle's inequality for the geodesic flow in non-compact manifolds with Anosov geodesic flow and some assumptions on the curvature. In the same way, we obtain Pesin's formula for Anosov geodesic flow in non-compact manifolds with finite volume.