Partial hyperbolicity and foliations in $\mathbb{T}^3$
Dynamical Systems
2014-07-15 v2 Geometric Topology
Abstract
We prove that dynamical coherence is an open and closed property in the space of partially hyperbolic diffeomorphisms of isotopic to Anosov. Moreover, we prove that strong partially hyperbolic diffeomorphisms of 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.
Cite
@article{arxiv.1206.2860,
title = {Partial hyperbolicity and foliations in $\mathbb{T}^3$},
author = {Rafael Potrie},
journal= {arXiv preprint arXiv:1206.2860},
year = {2014}
}
Comments
45 pages, 4 figures. To appear in JMD. This version is more compact and includes many improvements clarifying proofs thanks to the referee report