arXiv subjects

Pablo Dávalos

Publications and source records attributed to Pablo Dávalos.

3 recordsLinked to original sources

arXiv2013

On annular maps of the torus and sublinear diffusion

There is a classification by Misiurewicz and Ziemian of elements in Homeo$_0(\mathbf{T}^2)$ by their rotation set $ρ$, according to wether $ρ$ is a point, a segment or a set with nonempty interior. A recent classification of nonwandering elements in Homeo$_0(\mathbf{T}^2)$ by Koropecki and Tal has been given, according to the itrinsic underlying ambient where the dynamics takes place: planar, annular and strictly toral maps. We study the link between these two classifications, showing that, even abroad the nonwandering setting, annular maps are characterized by rotation sets which are \textit{rational segments}. Also, we obtain information on the \textit{sublinear diffusion} of orbits in the -not very well understood- case that $ρ$ has nonempty interior.

math.DS↗

arXiv2013

Dynamical models for some torus homeomorphisms

It is well known that the rotation number of a circle homeomorphism defined by H. Poincaré allows to completely understand the dynamics of such a map from the topological point of view. In this paper, we collect some results concerning the existence of topological dynamical models associated to rotation sets of homeomorphisms of $\T^2$.

math.DS↗

arXiv2013

On torus homeomorphisms whose rotation set is an interval

We prove that for a torus homeomorphism isotopic to the identity and with a lift whose rotation set is an interval, either every rational point in the rotation set is realized by a periodic orbit, or there exists an annular, essential, periodic set. In the latter case we give a qualitative description of the dynamics.

math.DS↗