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ON ANNULAR MAPS OF THE TORUS AND SUBLINEAR DIFFUSION
Published online by Cambridge University Press: 23 June 2016
Abstract
A classical article by Misiurewicz and Ziemian (J. Lond. Math. Soc.40(2) (1989), 490–506) classifies the elements in Homeo$_{0}(\mathbf{T}^{2})$ by their rotation set $\unicode[STIX]{x1D70C}$, according to wether $\unicode[STIX]{x1D70C}$ 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 was given in (Invent. Math.196 (2014), 339–381), according to the intrinsic underlying ambient space 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 rational segments. Also, we obtain information on the sublinear diffusion of orbits in the—not very well understood—case that $\unicode[STIX]{x1D70C}$ has nonempty interior.
- Type
- Research Article
- Information
- Journal of the Institute of Mathematics of Jussieu , Volume 17 , Issue 4 , September 2018 , pp. 913 - 978
- Copyright
- © Cambridge University Press 2016
Footnotes
This work was partially supported by FAPESP-Brasil grant 2011/14122-5 and ITESO-México.
References
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