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arXiv · 1206.2860

Partial hyperbolicity and foliations in $\mathbb{T}^3$

Rafael Potrie
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Abstract

We prove that dynamical coherence is an open and closed property in the space of partially hyperbolic diffeomorphisms of $\mathbb{T}^3$ isotopic to Anosov. Moreover, we prove that strong partially hyperbolic diffeomorphisms of $\mathbb{T}^3$ are either dynamically coherent or have an invariant two-dimensional torus which is either contracting or repelling. We develop for this end some general results on codimension one foliations which may be of independent interest.

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Rafael Potrie. 2014-07-14. Partial hyperbolicity and foliations in $\mathbb{T}^3$. https://arxiv.org/abs/1206.2860

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