CHAOTIC PROPERTIES OF THE ELLIPTIC STADIUM

The elliptical stadium is a curve constructed by joining two half-elli pses, with half axes a > 1 and b = 1, by two straight segments of equa l length 2h. Donnay [6] has shown that if 1 < a < root 2 and if h is b ig enough, then the corresponding billiard map has a positive Lyapunov exponent almost everywhere; moreover, h --> infinity as a --> root 2. In this work we prove that if 1 < a < root 4-2 root 2, then h > 2a(2) root a(2)-1 assures the positiveness of a Lyapunov exponent. And we c onclude that, for these values of a and h, the elliptical stadium bill iard mapping is ergodic and has the K-property.