Entropy-expansiveness of Geodesic Flows on Closed Manifolds without Conjugate Points  

作　　者：Fei LIU Fang WANG 

机构地区：[1]College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China [2]School of Mathematical Sciences, Capital Normal University, Beijing 100048, P. R. China [3]Beijing Center for Mathematics and Information Interdisciplinary Sciences (BCMIIS), Beijing 100048, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2016年第4期507-520,共14页数学学报（英文版）

基　　金：supported by NSFC(Grant Nos.11301305 and 11571207);the grant "2012KYTD" from Shandong University of Science and Technology;supported by NSFC(Grant No.11101294);Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20111108120001);the grant of"Youxiu Rencai Peiyang Zizhu"(Class A)from the Beijing City

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.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.

关 键 词：Entropy-expansiveness geodesic flows manifolds without conjugate points 

分 类 号：O186.12[理学—数学]