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

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arxiv 1912.07825 v1 pith:AILKIWRV submitted 2019-12-17 math.DS

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

Dong Chen , Lien-Yung Kao , Kiho Park This is my paper
classification math.DS
keywords equilibriumstatesconditionfocalmanifoldspointspressureproperties
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We prove that for closed rank 1 manifolds without focal points the equilibrium states are unique for H\"older 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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