Asymptotic periodicity in outer billiards with contraction

Abstract

We show that for almost every $(P,\lambda )$ where $P$ is a convex polygon and $\lambda \in (0,1)$, the corresponding outer billiard about $P$ with contraction $\lambda$ is asymptotically periodic, i.e., has a finite number of periodic orbits and every orbit is attracted to one of them.

17 pages, 2 figures