Chaos in Cylindrical Stadium Billiards via a Generic nonlinear Mechanism

We describe conditions under which higher-dimensional billiard models in bounded, convex regions are fully chaotic, generalizing the Bunimovich stadium to dimensions above two. An example is a threedimensional stadium bounded by a cylinder and several planes; the combination of these elements may give rise to defocusing, allowing large chaotic regions in phase space. By studying families of marginallystable periodic orbits that populate the residual part of phase space, we identify conditions under which a nonlinear instability mechanism arises in their vicinity. For particular geometries, this mechanism rather induces stable nonlinear oscillations, including in the form of whispering-gallery modes.