The Hopf-Tsuji-Sullivan dichotomy on visibility manifolds without conjugate points

被引：1

作者：

Liu, Fei ^{[1
]}

Liu, Xiaokai ^{[2
]}

Wang, Fang ^{[3
]}

机构：

[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China

[2] Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China

[3] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2025年 / 423卷

关键词：

Geodesic flows; Hopf-Tsuji-Sullivan dichotomy; Patterson-Sullivan measure; Bowen-Margulis-Sullivan measure; RANK; 1; MANIFOLDS; GEODESIC-FLOWS; ASYMPTOTIC GEOMETRY; ERGODIC-THEORY; ENTROPY; SURFACES;

D O I：

10.1016/j.jde.2024.12.033

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we establish the Hopf-Tsuji-Sullivan dichotomy for geodesic flows on certain manifolds with no conjugate points: either the geodesic flow is conservative and ergodic, or it is completely dissipative and non-ergodic. We also show several equivalent conditions to the conservativity, such the Poincar & eacute; series diverges at the critical exponent, the conical limit set has full Patterson-Sullivan measure, etc. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页码：286 / 323

页数：38

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