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

Dong Chen; Lien Yung Kao; Kiho Park

doi:10.1016/j.aim.2021.107564

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

Dong Chen, Lien Yung Kao, Kiho Park

Mathematics

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2 Scopus citations

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.

Original language	English (US)
Article number	107564
Journal	Advances in Mathematics
Volume	380
DOIs	https://doi.org/10.1016/j.aim.2021.107564
State	Published - Mar 26 2021

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1016/j.aim.2021.107564

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title = "Properties of equilibrium states for geodesic flows over manifolds without focal points",

abstract = "We prove that for closed rank 1 manifolds without focal points the equilibrium states are unique for H{\"o}lder 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.",

author = "Dong Chen and Kao, {Lien Yung} and Kiho Park",

note = "Funding Information: The second author gratefully acknowledges support from the National Science Foundation Postdoctoral Research Fellowship under Grant Number DMS 1703554. Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

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AU - Park, Kiho

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PY - 2021/3/26

Y1 - 2021/3/26

N2 - 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.

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

Abstract

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