Linear Stability of Periodic Trajectories in Inverse Magnetic Billiards

Abstract

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 Ω and circular arcs outside Ω. 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.