平面二环面上某台球运动轨迹的统计
The statistics of the trajectory in a certain billiard in a flat two-torus
摘要：
我们考虑一个台球在穿孔环面通过删除一个小磁盘从二维平面环面，与轨迹开始从中心的穿刺。在这种情况下，相空间仅由速度的范围给出。我们证明了当穿孔的大小趋于零时，$[0,\infty)$上与第一个出口时间相关的概率测度是弱收敛的，并明确地计算了极限的密度。
英文摘要：
We consider a billiard in the punctured torus obtained by removing a small disk from the two-dimensional flat torus, with trajectory starting from the center of the puncture. In this case the phase space is given by the range of the velocity only. We prove that the probability measures on $[0,\infty)$ associated with the first exit time are weakly convergent when the size of the puncture tends to zero and explicitly compute the density of the limit.
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