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Remarks on Rigidity Properties of Conics

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Abstract

Inspired by the recent results toward Birkhoff conjecture (a rigidity property of billiards in ellipses), we discuss two rigidity properties of conics. The first one concerns symmetries of an analog of polar duality associated with an oval, and the second concerns properties of the circle map associated with an oval and two pencils of lines.

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ACKNOWLEDGMENTS

Many thanks to M. Lyubich for useful discussions.

Funding

The author was supported by NSF grant DMS-2005444.

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  1. Department of Mathematics, Pennsylvania State University, University Park, 16802, PA, USA

    Serge Tabachnikov

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  1. Serge Tabachnikov
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Correspondence to Serge Tabachnikov.

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The author declares that he has no conflicts of interest.

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MSC2010

53A20, 37E10

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Tabachnikov, S. Remarks on Rigidity Properties of Conics. Regul. Chaot. Dyn. 27, 18–23 (2022). https://doi.org/10.1134/S156035472201004X

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  • DOI: https://doi.org/10.1134/S156035472201004X

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