Entropy-expansiveness of geodesic flows on closed manifolds without conjugate points

被引：0
作者：
Fei Liu
Fang Wang
机构：
[1] Shandong University of Science and Technology,College of Mathematics and System Science
[2] Capital Normal University,School of Mathematical Sciences
[3] Beijing Center for Mathematics and Information Interdisciplinary Sciences (BCMIIS),undefined
来源：
Acta Mathematica Sinica, English Series | 2016年 / 32卷
关键词：
Entropy-expansiveness; geodesic flows; manifolds without conjugate points; 37B40; 37D40;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this article, we consider the entropy-expansiveness of geodesic flows on closed Riemannian manifolds without conjugate points. We prove that, if the manifold has no focal points, or if the manifold is bounded asymptote, then the geodesic flow is entropy-expansive. Moreover, for the compact oriented surfaces without conjugate points, we prove that the geodesic flows are entropy-expansive. We also give an estimation of distance between two positively asymptotic geodesics of an uniform visibility manifold.
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页码：507 / 520
页数：13
相关论文
共 34 条
[1]  
Anosov D. V.(1967)Geodesic flows on closed Riemannian manifolds of negative curvature Trudy Mat. Inst. Steklov. 90 1-235
[2]  
Bolsinov A. V.(2000)Integrable geodesic flows with positive topological entropy Invent. Math. 140 639-650
[3]  
Taimanov I. A.(1972)Entropy-expansive maps Trans. Amer. Math. Soc. 164 323-331
[4]  
Bowen R.(1994)Riemannian tori without conjugate points are flat Geom. Funct. Anal. 4 259-269
[5]  
Burago D.(2003)Invariant metric on nilmanifolds with positive topological entropy Geom. Dedi. 100 173-185
[6]  
Ivanov S.(1971)On the relations among various entropy characteristics of dynamical systems Math. USSR Izv. 5 337-378
[7]  
Butler L.(1973)Visibility manifolds Pacific J. Math. 46 45-109
[8]  
Dinaburg E. I.(2014)Topological entropy of minimal geodesics and volume growth on surfaces J. Modern Dynamics 8 75-91
[9]  
Eberlein P.(1958)A theorem of E. Hopf Michigan Math. J. 5 31-34
[10]  
O’Neill B.(1956)Geodesic instability Proc. Amer. Math. Soc. 7 438-448
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