台球问题的拓扑
Topology of billiard problems, I
摘要：
设$T\subset \R^{m+1}$是由光滑超曲面$X=\partial T$包围的严格凸域.本文给出了$T$中具有指定起始点$A\in X$、指定终点$B\in X$并在边界$X$上有指定反射数$n$的台球轨迹数的下界.我们应用了一种基于计算某些构型空间的上同调环的拓扑方法。
英文摘要：
Let $T\subset \R^{m+1}$ be a strictly convex domain bounded by a smooth hypersurface $X=\partial T$. In this paper we find lower bounds on the number of billiard trajectories in $T$ which have a prescribed intial point $A\in X$, a prescribed final point $B\in X$ and make a prescribed number $n$ of reflections at the boundary $X$. We apply a topological approach based on calculation of cohomology rings of certain configuration spaces.
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。
