Homeomorphisms of the annulus with a transitive lift
| dc.creator | Zanata, Salvador Addas | |
| dc.creator | Tal, Fabio Armando | |
| dc.date | 2008-11-18 | |
| dc.date.accessioned | 2026-07-07T10:19:25Z | |
| dc.date.available | 2026-07-07T10:19:25Z | |
| dc.description | Let $f$ be a homeomorphism of the closed annulus $A$ that preserves orientation, boundary components and that has a lift $\tilde f$ to the infinite strip $\tilde A$ which is transitive. We show that, if the rotation number of both boundary components of $A$ is strictly positive, then there exists a closed nonempty connected set $Γ\subset\tilde A$ such that $Γ\subset]-\infty,0]\times[0,1]$, $Γ$ is unlimited, the projection of $Γ$ to $A$ is dense, $Γ-(1,0)\subsetΓ$ and $\tilde{f}(Γ)\subset Γ.$ Also, if $p_1$ is the projection in the first coordinate in $\tilde A$, then there exists $d>0$ such that, for any $\tilde z\inΓ,$ $$\limsup_{n\to\infty}\frac{p_1(\tilde f^n(\tilde z))-p_1(\tilde z)}{n}<-d.$$ In particular, using a result of Franks, we show that the rotation set of any homeomorphism of the annulus that preserves orientation, boundary components, which has a transitive lift without fixed points in the boundary is an interval with 0 in its interior. | |
| dc.identifier | https://arxiv.org/abs/0811.3003 | |
| dc.identifier | http://arxiv.org/abs/0811.3003 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174498 | |
| dc.subject | Dynamical Systems | |
| dc.title | Homeomorphisms of the annulus with a transitive lift | |
| dc.type | text |