Codimension one partially hyperbolic diffeomorphisms with a uniformly compact center foliation

Doris Bohnet

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arXiv · 1303.4099

Codimension one partially hyperbolic diffeomorphisms with a uniformly compact center foliation

Doris Bohnet

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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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Doris Bohnet. 2013-03-17. Codimension one partially hyperbolic diffeomorphisms with a uniformly compact center foliation. https://arxiv.org/abs/1303.4099

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