Remarks on rigidity properties of conics
Serge Tabachnikov
TL;DR
This paper explores two rigidity properties of conics related to symmetries and circle maps, inspired by recent advances in billiard dynamics and the Birkhoff conjecture.
Contribution
It introduces new rigidity properties of conics involving polar duality and circle maps, extending understanding of conic symmetries.
Findings
Identifies symmetry properties of conics related to polar duality.
Analyzes properties of circle maps associated with ovals and line pencils.
Provides insights into rigidity phenomena of conic sections.
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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