Partial hyperbolicity and foliations in \mathbbT³

2012/06/13 by Rafael Potrie, Potrie, Rafael
Mathematics · #37C05 #37C20 #37C25 #37C29 #37D30 #57R30 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #math.DS #math.GT #msc:37C05 #msc:37C20 #msc:37C25 #msc:37C29 #msc:37D30 #msc:57R30

paper · pdf · doi:10.48550/arxiv.1206.2860

45 pages, 4 figures. To appear in JMD. This version is more compact and includes many improvements clarifying proofs thanks to the referee report

arxiv created 2014/07/14 · arxiv updated 2014/07/15

Abstract

We prove that dynamical coherence is an open and closed property in the space of partially hyperbolic diffeomorphisms of \mathbbT³ isotopic to Anosov. Moreover, we prove that strong partially hyperbolic diffeomorphisms of \mathbbT³ 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.

Related

• Dynamical coherence of partially hyperbolic diffeomorphisms of tori isotopic to Anosov
• Dynamical coherence of partially hyperbolic diffeomorphisms on nilmanifolds isotopic to Anosov
• Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part I: The dynamically coherent case
• Lyapunov exponents and regularity of invariant foliations for partially hyperbolic diffeomophisms on \mathbb T³
• Partially hyperbolic diffeormorphisms, ergodicity, and transverse foliations in dimension 3