- 96-353 Knill O.
- On nonconvex caustics of convex billiards
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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.