Straightening Billiard Trajectories in Flat Disks and Katok-Zemlyakov Construction

Autor:	Sağlam, İsmail
Rok vydání:	2019
Předmět:	Mathematics - Metric Geometry Mathematics - Dynamical Systems 51F99 37E35 57M50 32G15 7D40 37D50 30F10
Druh dokumentu:	Working Paper
Popis:	We provide a method to straighten each billiard trajectory in a flat disk. As an application, we show that for each point on the disk and for almost all directions, the closure of the corresponding billiard trajectory contains a vertex. We generalize Katok-Zemlyakov construction to the flat disks with rational angle data: for each rational flat disk we obtain a translation surface and a projection to the doubling of the disk. We calculate the Euler characteristics of this translation surface. Comment: 18 pages, 10 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1904.05186 Zobrazit plný text záznamu View this record from Arxiv