Integrable Billiards on a Minkowski Hyperboloid: Extremal Polynomials and Topology

Autor:	Dragovic, Vladimir, Gasiorek, Sean, Radnovic, Milena
Rok vydání:	2020
Předmět:	Mathematics - Dynamical Systems Mathematical Physics Nonlinear Sciences - Exactly Solvable and Integrable Systems 37C83 37J70 37J38 37J46 41A50 14H70
Druh dokumentu:	Working Paper
Popis:	We consider billiard systems within compact domains bounded by confocal conics on a hyperboloid of one sheet in the Minkowski space. We derive conditions for elliptic periodicity for such billiards. We describe the topology of those billiard systems in terms of Fomenko invariants. We provide then periodicity conditions in terms of functional Pell equations and related extremal polynomials. Several examples are computed in terms of elliptic functions and classical Chebyshev and Zolotarev polynomials, as extremal polynomials over one or two intervals. These results are contrasted with the cases of billiards in the Minkowski and the Euclidean planes. Comment: 32 pages, 9 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2010.07685 Zobrazit plný text záznamu View this record from Arxiv