Partially hyperbolic diffeomorphisms with a trapping property
Rafael Potrie
We study partially hyperbolic diffeomorphisms satisfying a trapping property which makes them look as if they were Anosov at large scale. We show that, as expected, they share several properties with Anosov diffeomorphisms. We construct an expansive quotient of the dynamics and study some dynamical consequences related to this quotient.
keywords: quasi-attractors classification Partial hyperbolicity dynamical coherence.
Partial hyperbolicity and foliations in $\mathbb{T}^3$
Rafael Potrie
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.
keywords: codimension-one foliations. dynamical coherence Partial hyperbolicity (pointwise) global product structure

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