{
  "id": "1210.4766",
  "version": "v3",
  "published": "2012-10-17T15:22:35.000Z",
  "updated": "2012-12-06T07:14:51.000Z",
  "title": "Quasi-Stability of Partially Hyperbolic Diffeomorphisms",
  "authors": [
    "Huyi Hu",
    "Yujun Zhu"
  ],
  "comment": "19 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "A partially hyperbolic diffeomorphism $f$ is structurally quasi-stable if for any diffeomorphism $g$ $C^1$-close to $f$, there is a homeomorphism $\\pi$ of $M$ such that $\\pi\\circ g$ and $f\\circ\\pi$ differ only by a motion $\\tau$ along center directions. $f$ is topologically quasi-stable if for any homeomorphism $g$ $C^0$-close to $f$, the above holds for a continuous map $\\pi$ instead of a homeomorphism. We show that any partially hyperbolic diffeomorphism $f$ is topologically quasi-stable, and if $f$ has $C^1$ center foliation $W^c_f$, then $f$ is structurally quasi-stable. As applications we obtain continuity of topological entropy for certain partially hyperbolic diffeomorphisms with one or two dimensional center foliation.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-12-06T07:14:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C20",
      "37C50",
      "37D30"
    ],
    "keywords": [
      "partially hyperbolic diffeomorphism",
      "quasi-stability",
      "dimensional center foliation",
      "homeomorphism",
      "center directions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.4766H"
    }
  }
}