Numerical study of a three-dimensional generalized stadium billiard

We study a generalized three-dimensional stadium billiard and present stron g numerical evidence that this system is completely chaotic. Tn this convex billiard chaos is generated by the defocusing mechanism. The construction of this billiard uses cylindrical components as the focusing elements and t hereby differs from the recent approach pioneered by Bunimovich and Rehacek [Commun. Math. Phys. 189, 729 (1997)]. We investigate the stability of low er-dimensional invariant manifolds and discuss bouncing ball modes.