  The elliptical stadium is a curve constructed by joining two half-ellipses,
with half axes a>1 and b=1, by two straight segments of equal length 2h. In
this work we find bounds on h, for a close to 1, to assure the positiveness of
a Lyapunov exponent. We conclude that, for these values of a and h, the
elliptical stadium billiard mapping is ergodic and has the K-property.
