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arXiv · 1710.02919

Gutkin billiard tables in higher dimensions and rigidity

Michael Bialy
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Abstract

E. Gutkin found a remarkable class of convex billiard tables in the plane which have a constant angle invariant curve. In this paper we prove that in dimension 3 only round sphere has such a property. For dimension greater than 3 it must be either a sphere or to have a very special geometric properties. In 2-dimensional case we prove a rigidity result for Gutkin billiard tables. This is done with the help of a new generating function introduced recently for billiards in our joint paper with A.E. Mironov. A formula for this generating function in higher dimensions is found.

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Michael Bialy. 2017-10-09. Gutkin billiard tables in higher dimensions and rigidity. https://doi.org/10.1088/1361-6544%2Faaaf4d

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