Open problems on billiards and geometric optics
type: Item
instance of: scholarly article
title: Open problems on billiards and geometric optics
author: Corentin Fierobe
author: Mark Levi
author: Alexander Plakhov
author: Misha Bialy
author: Alexey A. Glutsyuk
author: S. Tabachnikov
published in: Arnold Mathematical Journal
publication date: 2022-12-06T00:00:00Z
full work available at URL: https://arxiv.org/abs/2110.10750
Mathematics Subject Classification ID: 00A27
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37J39
Mathematics Subject Classification ID: 37A05
Mathematics Subject Classification ID: 37C83
Mathematics Subject Classification ID: 78A05
Mathematics Subject Classification ID: 52A10
zbMATH DE Number: 7627129
zbMATH Keywords: area-preserving maps
zbMATH Keywords: mathematical billiards
zbMATH Keywords: complete integrability
zbMATH Keywords: Newtonian aerodynamics
zbMATH Keywords: trapping light
MaRDI profile type: Publication
OpenAlex ID: W4206594408
cites work: Introducing symplectic billiards
cites work: On curves and polygons with the equiangular chord property
cites work: Nonsmooth convex caustics for Birkhoff billiards
cites work: Q3198453
cites work: Seules les quadriques admettent des caustiques
cites work: Angular billiard and algebraic Birkhoff conjecture
cites work: The Birkhoff-Poritsky conjecture for centrally-symmetric billiard tables
cites work: On Cusps of Caustics by Reflection: Billiard Variations on the Four Vertex Theorem and on Jacobi’s Last Geometric Statement
cites work: Complex caustics of the elliptic billiard
cites work: On the circumcenters of triangular orbits in elliptic billiard
cites work: Geodesics on an ellipsoid in Minkowski space
cites work: The Poisson summation formula for manifolds with boundary
cites work: Only ellipsoids have caustics
cites work: Capillary floating and the billiard ball problem
cites work: A billiards-like dynamical system for attacking chess pieces
cites work: Second term of the spectral asymptotic expansion of the Laplace-Beltrami operator on manifolds with boundary
cites work: On the local Birkhoff conjecture for convex billiards
cites work: On the integrability of Birkhoff billiards
cites work: Pseudo-Riemannian geodesics and billiards
cites work: Chess billiards
cites work: Geometry of thin films
cites work: Billiard transformations of parallel flows: a periscope theorem
cites work: The billiard ball problem on a table with a convex boundary - An illustrative dynamical problem. I. The invariant integral
cites work: On the Last Geometric Statement of Jacobi
cites work: Q5825924
cites work: Commuting dual billiard maps
cites work: Exact transverse line fields and projective billiards in a ball
cites work: Introducing projective billiards
cites work: Q5708384
DOI: 10.1007/S40598-022-00198-Y
description: scientific article; zbMATH DE number 7627129