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

被引：5

作者：

Chen, Dong ^{[1
]}

Kao, Lien-Yung ^{[2
]}

Park, Kiho ^{[3
]}

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[2] George Washington Univ, Dept Math, Washington, DC 20052 USA

[3] Univ Chicago, Dept Math, Chicago, IL 60637 USA

来源：

ADVANCES IN MATHEMATICS | 2021年 / 380卷

基金：

美国国家科学基金会;

关键词：

Equilibrium states; Manifolds without focal points; Non-uniform hyperbolicity;

D O I：

10.1016/j.aim.2021.107564

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that for closed rank 1 manifolds without focal points the equilibrium states are unique for Holder 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. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：34

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