Remarks on rigidity properties of conics
arXiv:2110.08909 · doi:10.1134/S156035472201004X
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.