$R^d$中$k$二次曲面内台球的Cayley型条件
Cayley-Type Conditions for Billiards within $k$ Quadrics in $R^d$
摘要：
引入了二次曲面内台球轨迹的外部反射、内部反射和签名的概念。本文给出了$R^d$中以$k$二次曲面为界的区域内台球的周期轨迹和$R^d$中以$k$椭球为界的台球有序对策的周期轨迹的Cayley型条件。在极限条件下，得到了描述$R^d$中二次曲面上台球系统周期轨线的条件。
英文摘要：
The notions of reflection from outside, reflection from inside and signature of a billiard trajectory within a quadric are introduced. Cayley-type conditions for periodical trajectories for the billiard in the region bounded by $k$ quadrics in $R^d$ and for the billiard ordered game within $k$ ellipsoids in $R^d$ are derived. In a limit, the condition describing periodic trajectories of billiard systems on a quadric in $R^d$ is obtained.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
