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A counter-example to the theorem of Hiemer and Snurnikov

Thierry Monteil
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Abstract

A planar polygonal billiard $¶$ is said to have the finite blocking property if for every pair $(O,A)$ of points in $¶$ there exists a finite number of ``blocking'' points $B_1, ..., B_n$ such that every billiard trajectory from $O$ to $A$ meets one of the $B_i$'s. As a counter-example to a theorem of Hiemer and Snurnikov, we construct a family of rational billiards that lack the finite blocking property.

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Thierry Monteil. 2004-08-31. A counter-example to the theorem of Hiemer and Snurnikov. https://doi.org/10.1023/b%3Ajoss.0000013974.81162.20

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