English

Codimension one partially hyperbolic diffeomorphisms with a uniformly compact center foliation

Dynamical Systems 2013-11-28 v2

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).

Keywords

Cite

@article{arxiv.1303.4099,
  title  = {Codimension one partially hyperbolic diffeomorphisms with a uniformly compact center foliation},
  author = {Doris Bohnet},
  journal= {arXiv preprint arXiv:1303.4099},
  year   = {2013}
}

Comments

34 pages

R2 v1 2026-06-21T23:43:24.063Z