Authors: Dragović, Vladimir 
Mironov, Andrey E.
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On Differential Equations of Integrable Billiard Tables
Journal: Acta Mathematica Sinica, English Series
Volume: 40
Issue: 1
First page: 417
Last page: 424
Issue Date: 1-Jan-2024
Rank: ~M23
ISSN: 1439-8516
DOI: 10.1007/s10114-024-2450-5
Abstract: 
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.
Keywords: 37C83 | 37J35 | 70H06 | piece-wise smooth surfaces | Polynomial first integrals | wire billiards
Publisher: Springer Link

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