A Lower Bound for Chaos on the Elliptical Stadium

The elliptical stadium is a plane region bounded by a curve constructed by joining two half-ellipses by two parallel segments of equal length. The billiard inside it, as a map, generates a two parameters family of dynamical systems. It is known that the system is ergodic for a certain region of the parameter space. In this work we study the stability of a particular family of periodic orbits obtaining good bounds for the chaotic zone.