On the dynamics of inverse magnetic billiards

Consider a strictly convex set omega in the plane, and a homogeneous, stationary magnetic field orthogonal to the plane whose strength is B on the complement of omega and 0 inside omega. The trajectories of a charged particle in this setting are straight lines concatenated with circular arcs of Larmor radius mu. We examine the dynamics of such a particle and call this inverse magnetic billiards. Comparisons are made to standard Birkhoff billiards and magnetic billiards, as some theorems regarding inverse magnetic billiards are consistent with each of these billiard variants while others are not.