96-353 Knill O.

On nonconvex caustics of convex billiards (1488K, uuencoded gzipped postscript) Aug 6, 96

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Abstract. There are billiard tables of constant width, for which the billiard map has invariant curves in the phase space which belong to continuous but nowhere differentiable caustics. We apply this to construct ruled surfaces which have a nowhere differentiable lines of striction. We use it also to get Riemannian metrics on the sphere such that the caustic belonging at least one point on the sphere is nowhere differentiable. For three dimensional billiards, we find three dimensional billiard surfaces with nonconvex rough caustics.

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