Unique equilibrium states for geodesic flows over surfaces without focal points
Dynamical Systems
2018-08-03 v1 Differential Geometry
Abstract
In this paper, we study dynamics of geodesic flows over closed surfaces of genus greater than or equal to 2 without focal points. Especially, we prove that there is a large class of potentials having unique equilibrium states, including scalar multiples of the geometric potential, provided the scalar is less than 1. Moreover, we discuss ergodic properties of these unique equilibrium states. We show these unique equilibrium states are Bernoulli, and weighted regular periodic orbits are equidistributed relative to these unique equilibrium states.
Cite
@article{arxiv.1808.00663,
title = {Unique equilibrium states for geodesic flows over surfaces without focal points},
author = {Dong Chen and Lien-Yung Kao and Kiho Park},
journal= {arXiv preprint arXiv:1808.00663},
year = {2018}
}
Comments
37 pages, 2 figures