On Differential Equations of Integrable Billiard Tables

On Differential Equations of Integrable Billiard Tables Full article

Journal

Acta Mathematica Sinica, English Series
ISSN: 1439-8516

Output data

Year: 2024, Volume: 40, Number: 1, Pages: 417-424 Pages count : 8 DOI: 10.1007/s10114-024-2450-5

Tags

Polynomial first integrals, wire billiards, piece-wise smooth surfaces

Authors

Dragović Vladimir ^1,2 , Mironov Andrey E. ^3,4

Affiliations

1	Department of Mathematical Sciences, The University of Texas at Dallas, Richardson, USA
2	Mathematical Institute SANU, Belgrade, Serbia
3	Novosibirsk State University, Novosibirsk, Russia
4	Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Funding (1)

Russian Science Foundation

21-41-00018

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 R3 with a first integral of degree one in velocities, and for finding a piece-wise smooth surface in R3 homeomorphic to a torus, being a table of a billiard admitting two additional first integrals.

Dragović V. , Mironov A.E.
On Differential Equations of Integrable Billiard Tables
Acta Mathematica Sinica, English Series. 2024. V.40. N1. P.417-424. DOI: 10.1007/s10114-024-2450-5 WOS Scopus РИНЦ OpenAlex

Submitted:	Jul 20, 2022
Accepted:	Jun 9, 2023
Published online:	Jan 5, 2024
Published print:	May 13, 2024

Web of science:	WOS:001136210300007
Scopus:	2-s2.0-85181449941
Elibrary:	65957598
OpenAlex:	W4390599632

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