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Unique equilibrium states for geodesic flows over surfaces without focal points

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arxiv 1808.00663 v1 pith:H6JEPR23 submitted 2018-08-02 math.DS math.DG

Unique equilibrium states for geodesic flows over surfaces without focal points

Dong Chen , Lien-Yung Kao , Kiho Park This is my paper
classification math.DS math.DG
keywords equilibriumstatesuniqueflowsfocalgeodesicpointsscalar
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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.

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