A pointwise ergodic theorem for Fuchsian groups

TL;DR

This paper proves an ergodic theorem for Cesaro averages of spherical averages in Fuchsian groups using Markovian coding and Bowen-Series coding techniques.

Contribution

It introduces a new ergodic theorem for Fuchsian groups based on advanced coding methods, extending previous results in the field.

Findings

Established convergence of Cesaro averages in Fuchsian groups

Applied Series' Markovian coding to ergodic theory

Utilized Bowen-Series coding for limit set analysis

Abstract

We use Series' Markovian coding for words in Fuchsian groups and the Bowen-Series coding of limit sets to prove an ergodic theorem for Cesaro averages of spherical averages in a Fuchsian group.