The Hopf-Tsuji-Sullivan Dichotomy on Visibility Manifolds Without Conjugate Points
Dynamical Systems
2023-06-08 v2
Abstract
In this article, we establish the Hopf-Tsuji-Sullivan dichotomy for geodesic flows on certain manifolds with no conjugate points: either the geodesic flow is conservative and ergodic, or it is completely dissipative and non-ergodic. We also show several equivalent conditions to the conservativity, such the Poincar\'e series diverges at the critical exponent, the conical limit set has full Patterson-Sullivan measure, etc.
Keywords
Cite
@article{arxiv.2305.00301,
title = {The Hopf-Tsuji-Sullivan Dichotomy on Visibility Manifolds Without Conjugate Points},
author = {Fei Liu and Xiaokai Liu and Fang Wang},
journal= {arXiv preprint arXiv:2305.00301},
year = {2023}
}
Comments
48 pages, 9 figures