Seminário

do

Semigrupo Dinâmico

Finite blocking property

on billiards and translation surfaces

Thierry Monteil

(Institut de Mathématiques de Luminy)

Sexta-feira

17 de Outubro
15:00
Anfiteatro 0.07

Abstract: 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 B₁, … , B_n such that every billiard trajectory from O to A meets one of the B_i's. Generalizing our construction of a counter-example to a theorem of Hiemer and Snurnikov, we show that the only regular n-gons that have the finite blocking property are the square, the equilateral triangle and the hexagon. Then we extend this result to translations surfaces by proving that the only Veech surfaces with the finite blocking property are the torus branched coverings. We also provide a local sufficient condition for a translation surface to fail the finite blocking property, that can be used in other contexts, like for example every L-shaped translation surface.