Wind-tree tiling billiards and their trapping strips

Abstract

We introduce a new dynamical system: the wind-tree tiling billiards. This system studies trajectories of a ray in Euclidean space which has a negative refractive index when encountering rectangular obstacles located at lattice points. We show that for almost every configuration of the system, trajectories with initial vertical direction are trapped in an infinite strip of the plane. This result is reminiscent of the propagation of light rays in Eaton lenses, as shown by Fr\k{a}czek and Schmoll.