Markov partitions for the geodesic flow on compact Riemann surfaces of constant negative curvature

Autor:	Hien, Huynh M.
Rok vydání:	2022
Předmět:	Mathematics - Differential Geometry Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	It is well-known that hyperbolic flows admit Markov partitions of arbitrarily small size. However, the constructions of Markov partitions for general hyperbolic flows are very abstract and not easy to understand. To establish a more detailed understanding of Markov partitions, in this paper we consider the geodesic flow on Riemann surfaces of constant negative curvature. We provide a rigorous construction of Markov partitions for this hyperbolic flow with explicit forms of rectangles and local cross sections. The local product structure is also calculated in detail. Comment: 9 pictures, 50 pages. Any comment is appreciated!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2203.14246 Zobrazit plný text záznamu View this record from Arxiv