Birkhoff billiards are insecure

Pages: 1035 - 1040, Volume 23, Issue 3, March 2009

doi:10.3934/dcds.2009.23.1035       Abstract        Full Text (125.0K)       Related Articles

Serge Tabachnikov - Department of Mathematics, Penn State University, University Park, PA 16802, United States (email)

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 $B$.

Keywords:  Birkhoff billiards, security, finite blocking, rational approximation, interpolating Hamiltonians
Mathematics Subject Classification:  Primary: 37J99, 37E99, 53C22, 78A05; Secondary: 11K60

Received: January 2008;      Revised: July 2008;      Published: November 2008.