论文标题
在可集成台球的微分方程上
On differential equations of integrable billiard tables
论文作者
论文摘要
我们引入了一种方法来找到定义表的功能的微分方程，以便相关的台球系统允许本地的第一积分。我们在三种情况下说明了这种方法：（本地）可集成的电线台球的情况，用于在$ {\ Mathbb r}^3 $中找到表面，并在速度中获得了第一个学位的第一个组成部分，并且可以在$ {\ Mathbb r}中找到零件的光滑表面，以便torus torus torus，一个台词。
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.
