Expansiveness for the geodesic and horocycle flows on compact Riemann surfaces of constant negative curvature

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:480

Article

Huynh Minh Hien¹ 

[1] Quy Nhon Univ, Dept Math & Stat, 170 An Duong Vuong, Quy Nhon, Vietnam

关键词: Expansiveness;    Geodesic flow;    Horocycle flow;   

DOI  :  10.1016/j.jmaa.2019.123425

来源: Elsevier

【 摘 要 】

We study expansive properties for the geodesic and horocycle flows on compact Riemann surfaces of constant negative curvature. It is well-known that the geodesic flow is expansive in the sense of Bowen-Walters and the horocycle flow is positive and negative separating in the sense of Gura. In this paper, we give a new proof of the expansiveness in the sense of Bowen-Walters for the geodesic flow and show that the horocycle flow is positive and negative kinematic expensive in the sense of Artigue as well as expansive in the sense of Katok-Hasselblatt but not expensive in the sense of Bowen-Walters. We also point out that the geodesic flow is neither positive nor negative separating. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free