Self-intersection Points of Billiard Trajectories in a Square with Small Pockets

Abstract

We study the self-intersections of billiard trajectories in a square with small pockets of size $\epsilon$ removed from its four corners. In particular, we establish an asymptotic formula for the $r$-th moment of the number of self-intersection points for each positive integer $r$, as well as the distribution of such points.

13 pages, 1 figure