CHAOTIC FOCUSING BILLIARDS IN HIGHER DIMENSIONS

Numerical computations of Lyapunov exponents for a class of three- and four-dimensional billiards whose boundary consists of flat and spheri cal components illustrate that such billiards are chaotic due to a def ocusing mechanism similar to the one which produces chaos in two-dimen sional billiards (e.g., in the stadium). These results demonstrate tha t recently established rigorous results or higher dimensional defocusi ng billiards are valid under substantially weaker assumptions.