Free curves and periodic points for torus homeomorphisms
| dc.creator | Kocsard, Alejandro | |
| dc.creator | Koropecki, Andres | |
| dc.date | 2007-12-05 | |
| dc.date.accessioned | 2026-07-07T08:47:24Z | |
| dc.date.available | 2026-07-07T08:47:24Z | |
| dc.description | We study the relationship between free curves and periodic points for torus homeomorphisms in the homotopy class of the identity. By free curve we mean a homotopically nontrivial simple closed curve that is disjoint from its image. We prove that every rational point in the rotation set is realized by a periodic point provided that there is no free curve and the rotation set has empty interior. This gives a topological version of a theorem of Franks. Using this result, and inspired by a theorem of Guillou, we prove a version of the Poincaré-Birkhoff Theorem for torus homeomorphisms: in the absence of free curves, either there is a fixed point or the rotation set has nonempty interior. | |
| dc.description | to appear in Ergodic Theory and Dynamical Systems | |
| dc.identifier | https://arxiv.org/abs/0712.0643 | |
| dc.identifier | http://arxiv.org/abs/0712.0643 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143584 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37E30; 37E45 | |
| dc.title | Free curves and periodic points for torus homeomorphisms | |
| dc.type | text |