A counter-example to the theorem of Hiemer and Snurnikov

Details A counter-example to the theorem of Hiemer and Snurnikov A counter-example to the theorem of Hiemer and Snurnikov

2004-08-31

arxiv.org/abs/math/0408431v1

Mathematics

Dynamical Systems

5 pages, 3 figures

Scientific paper

10.1023/B:JOSS.0000013974.81162.

A planar polygonal billiard $\P$ is said to have the finite blocking property if for every pair $(O,A)$ of points in $\P$ 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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