von-Neumann and Birkhoff ergodic theorems for negatively curved groups
Dynamical Systems
2013-03-19 v1
Abstract
We prove maximal inequalities for concentric ball and spherical shell averages on a general Gromov hyperbolic group, in arbitrary probability preserving actions of the group. Under an additional condition, satisfied for example by all groups acting isometrically and properly discontinuously on CAT(-1) spaces, we prove a pointwise ergodic theorem with respect to a sequence of probability measures supported on concentric spherical shells.
Cite
@article{arxiv.1303.4109,
title = {von-Neumann and Birkhoff ergodic theorems for negatively curved groups},
author = {Lewis Bowen and Amos Nevo},
journal= {arXiv preprint arXiv:1303.4109},
year = {2013}
}