Pseudo-Euclidean Billiards within Confocal Curves on the Hyperboloid of One Sheet

Autor:	Gasiorek, Sean, Radnovic, Milena
Rok vydání:	2020
Předmět:	Mathematics - Dynamical Systems 70H06 70H12 37J35 37J46 (Primary) 14H70 37J38 37J39 (Secondary)
Druh dokumentu:	Working Paper
DOI:	10.1016/j.geomphys.2020.104032
Popis:	We consider a billiard problem for compact domains bounded by confocal conics on a hyperboloid of one sheet in the Minkowski space. We show that there are two types of confocal families in such setting. Using an algebro-geometric integration technique, we prove that the billiard within generalized ellipses of each type is integrable in the sense of Liouville. Further, we prove a generalization of the Poncelet theorem and derive Cayley-type conditions for periodic trajectories and explore geometric consequences. Comment: 30 pages, 15 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2008.06158 Zobrazit plný text záznamu View this record from Arxiv