Numerical study of a three-dimensional generalized stadium billiard

Abstract

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

4 pages, 1 PS-figure, revised version

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• 3D billiards: visualization of regular structures and trapping of chaotic trajectories
• Bouncing ball orbits and symmetry breaking effects in a three-dimensional chaotic billiard
• Morphological Image Analysis of Quantum Motion in Billiards
• Stable and unstable regimes in higher-dimensional convex billiards with cylindrical shape
• Metric deformation and boundary value problems in 3D
• Boundary perturbations and the Helmholtz equation in three dimensions
• Chaos in cylindrical stadium billiards via a generic nonlinear mechanism