Finite blocking property versus pure periodicity
| dc.creator | Monteil, Thierry | |
| dc.date | 2004-06-24 | |
| dc.date | 2008-03-07 | |
| dc.date.accessioned | 2026-07-07T09:25:19Z | |
| dc.date.available | 2026-07-07T09:25:19Z | |
| dc.description | A 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. | |
| dc.description | 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" | |
| dc.identifier | https://arxiv.org/abs/math/0406506 | |
| dc.identifier | http://arxiv.org/abs/math/0406506 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156363 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37D50; 37C27; 57M12; 51E21; 37E35; 32G15 | |
| dc.title | Finite blocking property versus pure periodicity | |
| dc.type | text |