Abstract
We consider the billiard ball problem in the interior of a plane closed convexC 1 curve which is piecewiseC 2. If the curvature has a discontinuity, then the boundary is unstable, i.e. no caustics exist near the boundary. However, in the interior there can exist caustics, as we show by an example.
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Communicated by J.-P. Eckmann
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Hubacher, A. Instability of the boundary in the billiard ball problem. Commun.Math. Phys. 108, 483–488 (1987). https://doi.org/10.1007/BF01212321
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DOI: https://doi.org/10.1007/BF01212321