No-slip billiards in dimension two

TL;DR

This paper studies no-slip billiards involving rotating disks exchanging momentum, revealing non-ergodic behavior and challenging traditional chaos generation methods in billiard systems.

Contribution

It provides new results on orbit periodicity and boundedness, and demonstrates non-ergodic features through computer simulations.

Findings

Certain polygons are not ergodic in no-slip billiards

Computer phase portraits show non-ergodic, potentially chaotic behavior

Standard chaos techniques may not apply to no-slip billiard systems

Abstract

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.