Three-Period Orbits in Billiards on the Surfaces of Constant Curvature

Autor:	Blumen, Victoria, Kim, Ki Yeun, Nance, Joe, Zharnitsky, Vadim
Rok vydání:	2011
Předmět:	Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	An approach due to Wojtkovski [9], based on the Jacobi fields, is applied to study sets of 3-period orbits in billiards on hyperbolic plane and on two-dimensional sphere. It is found that the set of 3-period orbits in billiards on hyperbolic plane, as in the planar case, has zero measure. For the sphere, a new proof of Baryshnikov's theorem is obtained which states that 3-period orbits can form a set of positive measure provided a natural condition on the orbit length is satisfied. Comment: 10 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1108.0987 Zobrazit plný text záznamu View this record from Arxiv