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arXiv · 1912.07825

Properties of equilibrium states for geodesic flows over manifolds without focal points

Dong Chen·Lien-Yung Kao·Kiho Park
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Abstract

We prove that for closed rank 1 manifolds without focal points the equilibrium states are unique for Hölder potentials satisfying the pressure gap condition. In addition, we provide a criterion for a continuous potential to satisfy the pressure gap condition. Moreover, we derive several ergodic properties of the unique equilibrium states including the equidistribution and the K-property.

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Dong Chen, Lien-Yung Kao, Kiho Park. 2019-12-17. Properties of equilibrium states for geodesic flows over manifolds without focal points. https://doi.org/10.1088/1361-6544%2Fab5c06

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