{
  "id": "math/0609365",
  "version": "v1",
  "published": "2006-09-13T18:46:11.000Z",
  "updated": "2006-09-13T18:46:11.000Z",
  "title": "Some results on the integrability of the center bundle for partially hyperbolic diffeomorphisms",
  "authors": [
    "F. Rodriguez Hertz",
    "MA. Rodriguez Hertz",
    "R. Ures"
  ],
  "comment": "8 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove, for f a partially hyperbolic diffeomorphism with center dimension one, two results about the integrability of its central bundle. On one side, we show that if the non wandering set of f is the whole manifold, and the manifold is 3 dimensional, then the absence of periodic points implies the unique integrability of the central bundle. On the opposite side, we prove that any periodic point p of large period n has an f n invariant center manifold, everywhere tangent to the center bundle. We also obtain, as a consequence of the last result, that there is an open and dense subset of C 1 robustly transitive and partially hyperbolic diffeomorphisms with center dimension one, such that either the strong stable or the strong unstable foliation is minimal. This generalizes a result obtained in BDU for 3 dimensional manifolds to any dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-13T18:46:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D30",
      "37D10"
    ],
    "keywords": [
      "partially hyperbolic diffeomorphism",
      "center bundle",
      "integrability",
      "central bundle",
      "center dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9365R"
    }
  }
}