Billiards in generic convex bodies have positive topological entropy

Autor:	Bessa, Mário, Del Magno, Gianluigi, Dias, João Lopes, Gaivão, José Pedro, Torres, Maria Joana
Rok vydání:	2022
Předmět:	Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	We show that there exists a $C^2$ open dense set of convex bodies with smooth boundary whose billiard map exhibits a non-trivial hyperbolic basic set. As a consequence billiards in generic convex bodies have positive topological entropy and exponential growth of the number of periodic orbits. Comment: 33 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2201.01362 Zobrazit plný text záznamu View this record from Arxiv