Unique equilibrium states for geodesic flows over surfaces without focal points
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, including the Bernoulli property and the fact that weighted regular periodic orbits are equidistributed relative to these unique equilibrium states.
This is an author-created, un-copyedited version of an article accepted for publication/published in 'Nonlinearity'. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6544/ab5c06
|Work Title||Unique equilibrium states for geodesic flows over surfaces without focal points|
|License||CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives)|
|Publication Date||February 5, 2020|
|Publisher Identifier (DOI)||
|Deposited||January 13, 2022|
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