English

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.

Keywords

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

R2 v1 2026-06-22T11:09:19.186Z