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The elliptical stadium is a plane region bounded by a curve constructed by joining two half-ellipses, with half axes
a > 1 and
b = 1, by two parallel segments of equal length 2
h.
Donnay [Comm. Math. Phys. 141 (1991) 225–257] proved that if
1 < a <
2
and if
h is large enough then the corresponding billiard map has non-vanishing Lyapunov exponents almost everywhere; moreover
h → ∞
as a →
2
. In a previous paper [Markarian et al. Comm. Math. Phys. 174 (1996) 661–679] we 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 chaotic zone for any value of
a <
2
.