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Zbl 1076.37029
Monteil, Thierry
On the finite blocking property. (English)
[J] Ann. Inst. Fourier 55, No. 4, 1195-1217 (2005). ISSN 0373-0956; ISSN 1777-5310/e

A polygon is said to have the finite blocking property if every billiard orbit connecting two arbitrary points $A$ and $O$ on the boundary must intersect a finite set of boundary points. Such set depends on $A$ and $O$, but does not contain them. The author proves -- among other things -- that the only regular polygons having such property are the triangle, the square, and the hexagon. This definition extends to translation surfaces, for which some useful characterizations are derived.
[Franco Vivaldi (London)]

MSC 2000:: *37E35 Flows on surfaces
37D50 Hyperbolic systems with singularities
37J10 Symplectic mappings, fixed points
37A10 One-parameter continuous families of measure-preserving transformations
30F30 Differentials on Riemann surfaces
51M99 Real and complex geometry

Keywords: blocking property; polygonal billiards; regular polygons; translation surfaces; Veech surfaces; torus branched covering; illumination; quadratic differentials

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