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

28 Nov 2017  ·  Kaloshin Vadim, Zhang Jianlu ·

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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Dynamical Systems