# American Institute of Mathematical Sciences

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 & Continuous Dynamical Systems - A, 2009, 23 (3) : 1035-1040. doi: 10.3934/dcds.2009.23.1035
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