Codimension one partially hyperbolic diffeomorphisms with a uniformly compact center foliation

2013/03/17 by Doris Bohnet, Bohnet, Doris · 1 citation
Mathematics · #37C15 #37C40 #37D30 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37C15 #msc:37C40 #msc:37D30

paper · pdf · doi:10.48550/arxiv.1303.4099

34 pages

arxiv created 2013/11/27 · arxiv updated 2013/11/28

Abstract

We consider a partially hyperbolic C1-diffeomorphism f on a smooth compact manifold M with a uniformly compact f-invariant center foliation. We show that if the unstable bundle is one-dimensional and oriented, then the holonomy of the center foliation vanishes everywhere, the quotient space of the center foliation is a torus and f induces a hyperbolic automorphism on it, in particular, f is centrally transitive. We actually obtain further interesting results without restrictions on the unstable, stable and center dimension: we prove a kind of spectral decomposition for the chain recurrent set of the quotient dynamics, and we establish the existence of a holonomy invariant family of measures on the unstable leaves (Margulis measure).

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• Entropy Flexibility of Dynamical Systems

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