On nonconvex caustics of convex billiards

Oliver Knill

March 12, 1997, appeared in the journal Elemente der Mathematics , 1998

Abstract	We illustrate the dynamics of billiards in tables of constant width. Caustics of such tables can be nowhere differentiable and are related to caustics appearing in differential geometry.

Introduction Convex billiard tables Caustics of convex billiards Caustics of tables of constant width Nowhere differentiable caustics Nowhere differentiable lines of striction of ruled surfaces Nowhere differentiable caustics on spheres Are there examples of fractal caustics? Caustics and billiards in three dimensions References About this document ...

The following Mathematica programs were used for making the illustrations in the article. I wrote them ad hoc but the procedures should be readable. The procedures are mainly undocumented. If you like some of the pictures, have a look! Caustic.m Dynamic.m LpBill.m Geodesic.m ThreeDim.m WaveFront.m