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July  2009, 23(3): 1035-1040. doi: 10.3934/dcds.2009.23.1035

Birkhoff billiards are insecure

Serge Tabachnikov 1,

1. 

Department of Mathematics, Penn State University, University Park, PA 16802

Received  January 2008 Revised  July 2008 Published  November 2008

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: security, Birkhoff billiards, interpolating Hamiltonians, finite blocking, rational approximation.
Mathematics Subject Classification: Primary: 37J99, 37E99, 53C22, 78A05; Secondary: 11K60.
Citation: Serge Tabachnikov. Birkhoff billiards are insecure. Discrete & Continuous Dynamical Systems, 2009, 23 (3) : 1035-1040. doi: 10.3934/dcds.2009.23.1035
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