On the ergodicity of geodesic flows on surfaces without focal points

被引：2
作者：
Wu, Weisheng [1 ]
Liu, Fei [2 ]
Wang, Fang [3 ,4 ]
机构：
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
[2] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China
[3] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China
[4] Beijing Ctr Math & Informat Interdisciplinary Sci, Beijing 100048, Peoples R China
来源：
ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2023年 / 43卷 / 12期
关键词：
ergodicity; geodesic flow; no focal points; non-uniform hyperbolicity; MANIFOLDS;
D O I：
10.1017/etds.2022.114
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the ergodicity of the geodesic flows on surfaces with no focal points. Let M be a smooth connected and closed surface equipped with a C-infinity Riemannian metric g, whose genus g >= 2. Suppose that (M, g) has no focal points. We prove that the geodesic flow on the unit tangent bundle of M is ergodic with respect to the Liouville measure, under the assumption that the set of points on M with negative curvature has at most finitely many connected components.
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页码：4226 / 4248
页数：23
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