Partially hyperbolic diffeomorphisms with one-dimensional neutral center on 3-manifolds

Jinhua Zhang

Published 2017-01-22Version 1

We prove that for any partially hyperbolic diffeomorphism with one dimensional neutral center on a 3-manifold, the center stable and center unstable foliations are complete; moreover, each leaf of center stable and center unstable foliations is a cylinder, a M$\ddot{o}$bius band or a plane. The structure of the new partially hyperbolic diffeomorphisms in [BZ] is studied. The examples in [BZ] are obtained by composing the time $m$-map (for $m$ large) of a non-transitive Anosov flow $\phi_t$ on an orientable 3-manifold with Dehn twists along some transverse tori, and the examples are partially hyperbolic with one-dimensional neutral center. We prove that the center foliation gives a topologically Anosov flow which is topologically equivalent to $\phi_t$. We also prove that for the example in [BPP], the center stable and center unstable foliations are robustly complete.