Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

A pointwise ergodic theorem for Fuchsian groups

ALEXANDER I. BUFETOVa1 and CAROLINE SERIESa2

a1 The Steklov Institute of Mathematics, Russian Academy of Sciences, Gubkina Str. 8, 119991, Moscow, Russia. e-mail: aib1@rice.edu

a2 Mathematics Institute, University of Warwick, Coventry CV4 7AL. e-mail: C.M.Series@warwick.ac.uk

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 Cesàro averages of spherical averages in a Fuchsian group.

(Received October 26 2010)

(Revised February 04 2011)

(Online publication April 27 2011)