Ergodicity of the geodesic flow for groups with a contracting element
Dynamical Systems
2025-10-28 v4 Group Theory
Metric Geometry
Abstract
In this article we investigate the dynamical properties of the geodesic flow for a proper metric space endowed with a proper action by isometries of a group with a contracting element. We show that the existence of a contracting isometry is a sufficient evidence of negative curvature to carry in this context various results borrowed from hyperbolic geometry. In particular, we extend the so-called Hopf-Tsuji-Sullivan dichotomy proving that the geodesic flow is either conservative and ergodic or dissipative.
Cite
@article{arxiv.2303.01390,
title = {Ergodicity of the geodesic flow for groups with a contracting element},
author = {Rémi Coulon},
journal= {arXiv preprint arXiv:2303.01390},
year = {2025}
}
Comments
75 pages