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

Kaloshin, Vadim; Koudjinan, Edmond

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

Kaloshin V, Koudjinan E. Non co-preservation of the 1/2 and 1/(2l+1)-rational caustics along deformations of circles. arXiv, 2107.03499.

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https://doi.org/10.48550/arXiv.2107.03499 [Submitted Version]

DOI

10.48550/arXiv.2107.03499

Preprint | Submitted | English

Author

Kaloshin, Vadim^ISTA ; Koudjinan, Edmond^ISTA

Corresponding author has ISTA affiliation

Department

Kaloshin Group

Abstract

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

Publishing Year

2021

Date Published

2021-07-07

Journal Title

arXiv

Article Number

2107.03499

IST-REx-ID

9435

Cite this

Kaloshin V, Koudjinan E. Non co-preservation of the 1/2 and 1/(2l+1)-rational caustics along deformations of circles. arXiv. doi:10.48550/arXiv.2107.03499

Kaloshin, V., & Koudjinan, E. (n.d.). Non co-preservation of the 1/2 and 1/(2l+1)-rational caustics along deformations of circles. arXiv. https://doi.org/10.48550/arXiv.2107.03499

Kaloshin, Vadim, and Edmond Koudjinan. “Non Co-Preservation of the 1/2 and 1/(2l+1)-Rational Caustics along Deformations of Circles.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2107.03499.

V. Kaloshin and E. Koudjinan, “Non co-preservation of the 1/2 and 1/(2l+1)-rational caustics along deformations of circles,” arXiv. .

Kaloshin V, Koudjinan E. Non co-preservation of the 1/2 and 1/(2l+1)-rational caustics along deformations of circles. arXiv, 2107.03499.

Kaloshin, Vadim, and Edmond Koudjinan. “Non Co-Preservation of the 1/2 and 1/(2l+1)-Rational Caustics along Deformations of Circles.” ArXiv, 2107.03499, doi:10.48550/arXiv.2107.03499.

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