Nonsmooth convex caustics for Birkhoff billiards

DOI10.2140/pjm.2018.295.257zbMath1390.37068arXiv1708.04280OpenAlexW3102321652MaRDI QIDQ1744249

Maxim Arnold, Misha Bialy

Publication date: 23 April 2018

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.04280

zbMATH Keywords

Birkhoff billiardconvex causticstring construction

Mathematics Subject Classification ID

Related Items (6)

The Birkhoff-Poritsky conjecture for centrally-symmetric billiard tables ⋮ On the fragility of periodic tori for families of symplectic twist maps ⋮ A survey on polynomial in momenta integrals for billiard problems ⋮ On the integrability of Birkhoff billiards ⋮ Open problems on billiards and geometric optics ⋮ Inverse problems and rigidity questions in billiard dynamics

Cites Work

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• An integrable deformation of an ellipse of small eccentricity is an ellipse
• Numerical exploration of a hexagonal string billiard
• On nonconvex caustics of convex billiards
• Convex billiards and a theorem by E. Hopf
• Geometry of geodesics for convex billiards and circular billards.
• Instability of the boundary in the billiard ball problem

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