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.