{
  "id": "1405.1492",
  "version": "v1",
  "published": "2014-05-07T02:44:34.000Z",
  "updated": "2014-05-07T02:44:34.000Z",
  "title": "Open sets of diffeomorphisms with trivial centralizer in the $C^1$ topology",
  "authors": [
    "Lennard Bakker",
    "Todd Fisher"
  ],
  "comment": "27 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "On the torus of dimension $2$, $3$, or $4$, we show that the subset of diffeomorphisms with trivial centralizer in the $C^1$ topology has nonempty interior. We do this by developing two approaches, the fixed point and the odd prime periodic point, to obtain trivial centralizer for an open neighbourhood of Anosov diffeomorphisms arbitrarily near certain irreducible hyperbolic toral automorphism.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-07T02:44:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R11",
      "11R16",
      "11R27",
      "37C05",
      "37C20",
      "37C25",
      "37D05",
      "37D20"
    ],
    "keywords": [
      "trivial centralizer",
      "open sets",
      "odd prime periodic point",
      "irreducible hyperbolic toral automorphism",
      "nonempty interior"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/27/12/2869",
      "journal": "Nonlinearity",
      "year": 2014,
      "month": "Dec",
      "volume": 27,
      "number": 12,
      "pages": 2869
    },
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014Nonli..27.2869B"
    }
  }
}