Unique ergodicity of the horocyclic flow on nonpositively curved surfaces
Dynamical Systems
2023-01-04 v2
Abstract
On the unit tangent bundle of a nonflat compact nonpositively curved surface, we prove that there is a unique probability Borel measure invariant by a horocyclic flow which gives full measure to the set of rank vectors recurrent by the geodesic flow. If we assume in addition that the surface has no flat strips, we show that the horocyclic flow is uniquely ergodic. These results are valid for any parametrization of the horocyclic flow.
Keywords
Cite
@article{arxiv.2106.11572,
title = {Unique ergodicity of the horocyclic flow on nonpositively curved surfaces},
author = {Sergi Burniol Clotet},
journal= {arXiv preprint arXiv:2106.11572},
year = {2023}
}