On the ergodicity of geodesic flows on surfaces without focal points

被引：1

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.

引用

页码：4226 / 4248

页数：23

共 50 条

[21] Dynamics of geodesic flows on hyperbolic compact surfaces with some elliptic points
Dastjerdi, Dawoud Ahmadi
Lamei, Sanaz
DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2014, 29 (04): : 537 - 568
[22] DISPERSING BILLIARDS WITHOUT FOCAL POINTS ON SURFACES ARE ERGODIC
KRAMLI, A
SIMANYI, N
SZASZ, D
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1989, 125 (03) : 439 - 457
[23] Ergodicity of Geodesic Flows on Incomplete Negatively Curved Manifolds
Burns, Keith
Masur, Howard
Matheus, Carlos
Wilkinson, Amie
ERGODIC THEORY AND NEGATIVE CURVATURE, 2017, 2164 : 175 - 208
[24] TRANSITIVITY OF FINSLER GEODESIC FLOWS OF COMPACT SURFACES WITHOUT CONJUGATE POINTS AND HIGHER GENUS, AND APPLICATIONS TO FINSLER RIGIDITY PROBLEMS
Chimenton, Alessandro G.
Comes, Jose Barbosa
Ruggiero, Rafael O.
HOUSTON JOURNAL OF MATHEMATICS, 2015, 41 (02): : 523 - 551
[25] Dual points of hyperbolic geodesics of square integrable geodesic flows on closed surfaces
Matveev, VS
Topalov, P
VESTNIK MOSKOVSKOGO UNIVERSITETA SERIYA 1 MATEMATIKA MEKHANIKA, 1998, (01): : 60 - 62
[26] INTEGRABLE GEODESIC FLOWS ON SURFACES
Bialy, Misha
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2010, 20 (02) : 357 - 367
[27] HOROCYCLE FLOWS ON CERTAIN SURFACES WITHOUT CONJUGATE POINTS
EBERLEIN, P
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1977, 233 (OCT) : 1 - 36
[28] FLOWS WITHOUT WANDERING POINTS ON COMPACT CONNECTED SURFACES
Cobo, Milton
Gutierrez, Carlos
Llibre, Jaume
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 362 (09) : 4569 - 4580
[29] Integrable Geodesic Flows on Surfaces
Misha Bialy
Geometric and Functional Analysis, 2010, 20 : 357 - 367
[30] Entropy-expansiveness of geodesic flows on closed manifolds without conjugate points
Fei Liu
Fang Wang
Acta Mathematica Sinica, English Series, 2016, 32 : 507 - 520

← 1 2 3 4 5 →