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

共 32 条

[21]

Katok A., 1982, ERGOD THEOR DYN SYST, V2, P339

[22] The uniqueness of the measure of maximal entropy for geodesic flows on rank 1 manifolds [J].

Knieper, G .

ANNALS OF MATHEMATICS, 1998, 148 (01) :291-314

[23]

Ledrappier F., 1977, Dynamical Systems, V50, P251

[24] ON THE PATTERSON-SULLIVAN MEASURE FOR GEODESIC FLOWS ON RANK 1 MANIFOLDS WITHOUT FOCAL POINTS [J].

Liu, Fei ;

Wang, Fang ;

Wu, Weisheng .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2020, 40 (03) :1517-1554

[25] Entropy-expansiveness of Geodesic Flows on Closed Manifolds without Conjugate Points [J].

Liu, Fei ;

Wang, Fang .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2016, 32 (04) :507-520

[26]

OSullivan JJ., 1976, J DIFFER GEOM, V11, P321

[27]

PARRY W, 1988, LECT NOTES MATH, V1342, P617

[28]

PARRY W, 1990, ASTERISQUE, P9

[29]

Pesin, 1977, IZV AKAD NAUK SSSR M, V41, P1252

[30]

Thompson D.J., 2019, ARXIV PREPRINT ARXIV

← 1 2 3 4 →