Non co-preservation of the $1/2$ & $1/(2l+1)$-rational caustics along deformations of circles

arXiv2107.03499MaRDI QIDQ6372248

Comlan E. Koudjinan, V. A. Kaloshin

Publication date: 7 July 2021

Abstract: For any given positive integer $l$, we prove that every plane deformation of a circle which preserves the $1/2$ and $1/(2l+1)$-rational caustics is trivial i.e. the deformation consists only of similarities (rescalings plus isometries).

Mathematics Subject Classification ID

Perturbation theories for problems in Hamiltonian and Lagrangian mechanics (70H09) Dynamical aspects of twist maps (37E40) Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods (37J51) Dynamical systems with singularities (billiards, etc.) (37C83)

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