CHAOS IN CYLINDRICAL STADIUM BILLIARDS VIA A GENERIC NONLINEAR MECHANISM

Abstract

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 three-dimensional 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 marginally-stable 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.