  We investigate the dynamics of no-slip billiards, a model in which small
rotating disks may exchange linear and angular momentum at collisions with the
boundary. We give new results on periodicity and boundedness of orbits which
suggest that a class of billiards (including all polygons) is not ergodic.
Computer generated phase portraits demonstrate non-ergodic features, suggesting
chaotic no-slip billiards cannot readily be constructed using the common
techniques for generating chaos in standard billiards.
