On differential equations of integrable billiard tables

Autor:	Dragović, Vladimir, Mironov, Andrey E.
Rok vydání:	2022
Předmět:	Mathematics - Dynamical Systems Mathematics - Differential Geometry Nonlinear Sciences - Exactly Solvable and Integrable Systems 37C83 37J70 53A17
Druh dokumentu:	Working Paper
Popis:	We introduce a method to find differential equations for functions which define tables, such that associated billiard systems admit a local first integral. We illustrate this method in three situations: the case of (locally) integrable wire billiards, for finding surfaces in ${\mathbb R}^3$ with a first integral of degree one in velocities, and for finding a piece-wise smooth surface in ${\mathbb R}^3$ homeomorphic to a torus, being a table of an integrable billiard. Comment: 9 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2207.09585 Zobrazit plný text záznamu View this record from Arxiv