On the number of periodic geodesics in rank 1 surfaces

TL;DR

This paper establishes a formula linking the topological pressure to the exponential growth rate of rank 1 periodic geodesics on compact rank 1 surfaces, extending previous work in the field.

Contribution

It generalizes a known result by deriving a new formula for topological pressure in the context of rank 1 geodesic flows.

Findings

Topological pressure equals exponential growth rate of periodic geodesics.

Provides a generalized formula extending prior results.

Enhances understanding of dynamical properties of rank 1 surfaces.

Abstract

We consider the geodesic flow of a compact connected rank 1 surface. We prove a formula for the topological pressure as the exponential growth rate of rank 1 periodic geodesics generalizing a previous result of K. Gelfert and B. Schapira [12].