TY - JOUR

T1 - On Differential Equations of Integrable Billiard Tables

AU - Dragović, Vladimir

AU - Mironov, Andrey E.

N1 - The research of AM has been partially supported by Russian Science Foundation (Grant No. 21-41-00018) and of VD by the Science Fund of Serbia (Grant Integrability and Extremal Problems in Mechanics, Geometry and Combinatorics, MEGIC, Grant No. 7744592), and the Simons Foundation (Grant No. 854861) Acknowledgements.

PY - 2024/1

Y1 - 2024/1

N2 - 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.

AB - 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.

KW - 37C83

KW - 37J35

KW - 70H06

KW - Polynomial first integrals

KW - piece-wise smooth surfaces

KW - wire billiards

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85181449941&origin=inward&txGid=91b016ad9d542492b367e0d3353db472

UR - https://www.mendeley.com/catalogue/87fb8085-adbf-3464-b899-6c0c52c92ce7/

U2 - 10.1007/s10114-024-2450-5

DO - 10.1007/s10114-024-2450-5

M3 - Article

VL - 40

SP - 417

EP - 424

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

SN - 1439-7617

IS - 1

ER -