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arXiv · 1711.10541

Coexistence of periodic-2 and periodic-3 caustics for nearly circular analytic billiard maps

Vadim Kaloshin·Jianlu Zhang
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Abstract

For symmetrically analytic deformation of the circle (with certain Fourier decaying rate), the necessary condition for the corresponding billiard map to keep the coexistence of periodic $2,3$ caustics is that the deformation has to be an isometric transformation.

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Vadim Kaloshin, Jianlu Zhang. 2017-11-28. Coexistence of periodic-2 and periodic-3 caustics for nearly circular analytic billiard maps. https://doi.org/10.3934/dcds.2019278

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