  We study dissipative polygonal outer billiards, i.e. outer billiards about
convex polygons with a contractive reflection law. We prove that dissipative
outer billiards about any triangle and the square are asymptotically periodic,
i.e. they have finitely many global attracting periodic orbits. A complete
description of the bifurcations of the periodic orbits as the contraction rates
vary is given. For the square billiard, we also show that the asymptotic
periodic behavior is robust under small perturbations of the vertices and the
contraction rates. Finally, we describe some numerical experiments suggesting
that dissipative outer billiards about regular polygon are generically
asymptotically periodic.
