On Differential Equations of Integrable Billiard Tables

被引：0

作者：

Vladimir DRAGOVIC ^{[1
,2
]}

Andrey E.MIRONOV ^{[3
,4
]}

机构：

[1] Department of Mathematical Sciences, The University of Texas at Dallas

[2] Mathematical Institute SANU

[3] Novosibirsk State University

[4] Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences

来源：

Acta Mathematica Sinica,English Series | 2024年 / 01期

基金：

俄罗斯科学基金会;

关键词：

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

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 R3with a first integral of degree one in velocities, and for finding a piece-wise smooth surface in R3homeomorphic to a torus,being a table of a billiard admitting two additional first integrals.

引用

页码：417 / 424

页数：8

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