Remarks on Rigidity Properties of Conics

Serge Tabachnikov

doi:10.1134/S156035472201004X

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.

Original language	English (US)
Pages (from-to)	18-23
Number of pages	6
Journal	Regular and Chaotic Dynamics
Volume	27
Issue number	1
DOIs	https://doi.org/10.1134/S156035472201004X
State	Published - Jan 2022

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

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10.1134/S156035472201004X

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title = "Remarks on Rigidity Properties of Conics",

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.",

author = "Serge Tabachnikov",

note = "Funding Information: The author was supported by NSF grant DMS-2005444. Publisher Copyright: {\textcopyright} 2022, Pleiades Publishing, Ltd.",

year = "2022",

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AB - 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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Remarks on Rigidity Properties of Conics

Abstract

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