Partially hyperbolic diffeomorphisms with compact center foliations

Details Partially hyperbolic diffeomorphisms with compact center foliations Partially hyperbolic diffeomorphisms with compact center foliations

2011-04-28

arxiv.org/abs/1104.5464v2

Mathematics

Dynamical Systems

22 pages, 1 figure. In the second version an error was corrected, the exposition was improved, new references added

Scientific paper

Let f:M->M be a partially hyperbolic diffeomorphism such that all of its center leaves are compact. We prove that Sullivan's example of a circle foliation that has arbitrary long leaves cannot be the center foliation of f. This is proved by thorough study of the accessible boundaries of the center-stable and the center-unstable leaves. Also we show that a finite cover of f fibers over an Anosov toral automorphism if one of the following conditions is met: 1. the center foliation of f has codimension 2, or 2. the center leaves of f are simply connected leaves and the unstable foliation of f is one-dimensional.

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