Some dynamical properties of the stadium billiard

We consider the dynamical properties of one kind of cyclically ordered orbits of the stadium billiard. We prove that the stadium billiard possesses infinitely many such orbits, that they are hyperbolic, and that their stable and unstable manifolds intersect transversely. Hence the stadium billiard contains a Smale horseshoe. We construct symbolic dynamics for these orbits and consider their sensitivity to choice of initial condition by studying their rotation numbers.