Periodic Bounce Orbits in Magnetic Billiard Systems.

This is an invitation to play magnetic billiards. We consider a billiard table that is an n-dimensional compact Riemannian manifold with smooth boundary. This is a generalization of the classical billiard game. In particular, we study periodic orbits on a prescribed energy level in the magnetic setup. We show that for sufficiently high energy values above the Man ̃ ́e critical value, there exists a periodic magnetic bounce orbit with bounded period.