A note on an ergodic theorem in weakly uniformly convex geodesic spaces
Dynamical Systems
2015-08-31 v2
Abstract
Karlsson and Margulis proved in the setting of uniformly convex geodesic spaces, which additionally satisfy a nonpositive curvature condition, an ergodic theorem that focuses on the asymptotic behavior of integrable cocycles of nonexpansive mappings over an ergodic measure-preserving transformation. In this note we show that this result holds true when assuming a weaker notion of uniform convexity.
Cite
@article{arxiv.1411.1095,
title = {A note on an ergodic theorem in weakly uniformly convex geodesic spaces},
author = {Laurentiu Leuştean and Adriana Nicolae},
journal= {arXiv preprint arXiv:1411.1095},
year = {2015}
}