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arXiv · 1704.04788

Rotational deviations and invariant pseudo-foliations for periodic point free torus homeomorphisms

Alejandro Kocsard·Fernanda Pereira-Rodrigues
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Abstract

This article deals with directional rotational deviations for non-wandering periodic point free homeomorphisms of the 2-torus which are homotopic to the identity. We prove that under mild assumptions, such a homeomorphism exhibits uniformly bounded rotational deviations in some direction if and only it leaves invariant a pseudo-foliation, a notion which is a slight generalization of classical one-dimensional foliations. To get these results, we introduce a novel object called $\tildeρ$-centralized skew-product and their associated stable sets at infinity.

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Alejandro Kocsard, Fernanda Pereira-Rodrigues. 2018-03-11. Rotational deviations and invariant pseudo-foliations for periodic point free torus homeomorphisms. https://doi.org/10.1007/s00209-018-2060-y

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