A LOWER-BOUND FOR CHAOS ON THE ELLIPTIC STADIUM

The elliptical stadium is a plane region bounded by a curve constructe d by joining two half-ellipses, with half axes a > 1 and b = 1, by two parallel segments of equal length 2h. Donnay [Comm. Math. Phys. 141 ( 1991) 225-257] proved that if 1 < a < root 2 and if h is large enough then the corresponding billiard map has non-vanishing Lyapunov exponen ts almost everywhere; moreover h --> infinity as a --> root 2. In a pr evious paper [Markarian et al. Comm. Math. Phys. 174 (1996) 661-679] w e found a bound for h assuring the K-property for these billiards, for values of a very close to 1. In this work we study the stability of a particular family of periodic orbits obtaining a new bound for the ch aotic zone for any value of a < root 2. Copyright (C) 1998 Elsevier Sc ience B.V.