Hyperbolic geometry and pointwise ergodic theorems
Dynamical Systems
2017-10-31 v2
Abstract
We establish pointwise ergodic theorems for a large class of natural averages on simple Lie groups of real-rank-one, going well beyond the radial case considered previously. The proof is based on a new approach to pointwise ergodic theorems, which is independent of spectral theory. Instead, the main new ingredient is the use of direct geometric arguments in hyperbolic space.
Cite
@article{arxiv.1509.09218,
title = {Hyperbolic geometry and pointwise ergodic theorems},
author = {Lewis Bowen and Amos Nevo},
journal= {arXiv preprint arXiv:1509.09218},
year = {2017}
}
Comments
Editorial changes only, some references added and typos corrected. No change in the main results and their proofs