{
  "id": "1701.06176",
  "version": "v1",
  "published": "2017-01-22T15:41:57.000Z",
  "updated": "2017-01-22T15:41:57.000Z",
  "title": "Partially hyperbolic diffeomorphisms with one-dimensional neutral center on 3-manifolds",
  "authors": [
    "Jinhua Zhang"
  ],
  "comment": "23 pages, 4 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-22T15:41:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "partially hyperbolic diffeomorphism",
      "one-dimensional neutral center",
      "center unstable foliations",
      "center stable",
      "dehn twists"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}