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

V. Kaloshin; C. E. Koudjinan

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arXiv · 2107.03499

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

V. Kaloshin·C. E. Koudjinan

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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).

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V. Kaloshin, C. E. Koudjinan. 2021-07-07. Non co-preservation of the $1/2$ & $1/(2l+1)$-rational caustics along deformations of circles. https://arxiv.org/abs/2107.03499

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