Birkhoff billiards are insecure

Serge Tabachnikov

doi:10.3934/dcds.2009.23.1035

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2009, Volume 23, Issue 3: 1035-1040. Doi: 10.3934/dcds.2009.23.1035

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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: July 2009

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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 $B$.

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Mathematics Subject Classification: Primary: 37J99, 37E99, 53C22, 78A05; Secondary: 11K60.

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