Linear stability of periodic trajectories in inverse magnetic billiards

We study the stability of periodic trajectories of planar inverse magnetic billiards, a dynamical system whose trajectories are straight lines inside a connected planar domain \Omega and (magnetic) Larmor arcs outside \Omega . Explicit examples are calculated in circles, ellipses, and the one parameter family of curves x^{2k} + y^{2k} = 1 . Comparisons are made to the linear stability of periodic billiard and magnetic billiard trajectories.