Birkhoff billiards are insecure

2007/05/23 by Serge Tabachnikov, Tabachnikov, Serge
Mathematics · #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #math.DG #math.DS

paper · pdf · doi:10.48550/arxiv.0705.3273

arxiv created 2007/05/23 · arxiv updated 2009/12/01

Abstract

We prove that every compact plane billiard, bounded by a smooth curve, is insecure: there exist pairs of points A,B such that no finite set of points can block all billiard trajectories from A to B.

Related

• Generic Absence of Finite Blocking for Interior Points of Birkhoff Billiards
• Integrable Billiards and Related Topics
• Angular Billiard and Algebraic Birkhoff conjecture
• Effective rigidity away from the boundary for centrally-symmetric billiards
• A challenger to elliptic billiards fails: String construction over convex polygons and the Birkhoff--Poritsky conjecture