2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156363A translation surface S is said to have the finite blocking property if for every pair (O,A) of points in S there exists a finite number of "blocking" points B_1,...,B_n such that every geodesic from O to A meets one of the B_i's. S is said to be purely periodic if the directional flow is periodic in each direction whose directional flow contains a periodic trajectory (this implies that S admits a cylinder decomposition in such directions). We will prove that finite blocking property implies pure periodicity. We will also classify the surfaces that have the finite blocking property in genus 2: such surfaces are exactly the torus branched coverings. Moreover, we prove that in every stratum, such surfaces form a set of null measure. In the Appendix, we prove that completely periodic translation surfaces form a set of null measure in every stratum.16 pages, 6 figures. v4 : minor changes to take referee's suggestions into account. In particular, an appendix is added with a proof of the following result: "In genus $g\geq 2$, the set of completely periodic translation surfaces has measure zero in every stratum"Dynamical Systems37D50; 37C27; 57M12; 51E21; 37E35; 32G15text