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

Birkhoff billiards are insecure

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 $B$.
Citation: Serge Tabachnikov. Birkhoff billiards are insecure. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 1035-1040. doi: 10.3934/dcds.2009.23.1035
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