Monteil, Thierry A counter-example to the theorem of Hiemer and Snurnikov. (English) Zbl 1058.37040 J. Stat. Phys. 114, No. 5-6, 1619-1623 (2004). Summary: 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 \(B_1,\dots,B_n\), such that every billiard trajectory from \(O\) to \(A\) meets one of the \(B_i\)’s. As a counter-example to a theorem of P. Hiemer and V. Snurnikov [J. Stat. Phys. 90, 453–466 (1998; Zbl 0995.37019)], we construct a family of rational billiards that lack the finite blocking property. Cited in 5 Documents MSC: 37J10 Symplectic mappings, fixed points (dynamical systems) (MSC2010) 37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010) 70H05 Hamilton’s equations Keywords:rational polygonal billiards; translation surfaces; blocking property Citations:Zbl 0995.37019 PDFBibTeX XMLCite \textit{T. Monteil}, J. Stat. Phys. 114, No. 5--6, 1619--1623 (2004; Zbl 1058.37040) Full Text: DOI arXiv