Abstract
A planar polygonal billiard \(\mathcal{P}\) is said to have the finite blocking property if for every pair (O, A) of points in \(\mathcal{P}\) 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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REFERENCES
P. Hiemer and V. Snurnikov, Polygonal billiards with small obstacles, J. Stat. Phys. 90:453–466 (1998).
H. Masur and S. Tabachnikov, Rational billiards and flat structures, Handbook on Dynamical Systems, Vol. 1A (North-Holland, Amsterdam, 2002), pp. 1015–1089.
T. Monteil, On the finite blocking property, preprint.
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Monteil, T. A Counter-Example to the Theorem of Hiemer and Snurnikov. Journal of Statistical Physics 114, 1619–1623 (2004). https://doi.org/10.1023/B:JOSS.0000013974.81162.20
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DOI: https://doi.org/10.1023/B:JOSS.0000013974.81162.20