论文标题
上限限制了固定台球的碰撞数量
Upper bound on the number of collisions of pinned billiard balls
论文作者
论文摘要
我们考虑“固定球”的系统，即具有固定位置和伪速度的球。伪速度根据与移动球之间完全弹性碰撞的速度相同的规则变化。不同对固定球的可能伪collix的时间以外源性方式选择。我们为在$ d $维空间中的$ n $固定球系统的最大伪collivision提供明确的上限。证明是基于对折叠的分析，即映射的映射，以形式化沿折痕折叠一张纸的想法。我们证明了对折叠点的点的轨道大小的上限。
We consider systems of "pinned balls," i.e., balls that have fixed positions and pseudo-velocities. Pseudo-velocities change according to the same rules as those for velocities of totally elastic collisions between moving balls. The times of possible pseudo-collisions for different pairs of pinned balls are chosen in an exogenous way. We give an explicit upper bound for the maximum number of pseudo-collisions for a system of $n$ pinned balls in a $d$-dimensional space. The proof is based on analysis of foldings, i.e., mappings that formalize the idea of folding a piece of paper along a crease. We prove an upper bound for the size of an orbit of a point subjected to foldings.
