{
  "id": "0711.4728",
  "version": "v2",
  "published": "2007-11-29T14:20:52.000Z",
  "updated": "2009-04-25T17:43:18.000Z",
  "title": "Rotation set and Entropy",
  "authors": [
    "Heber Enrich",
    "Nancy Guelman",
    "Audrey Larcanché",
    "Isabelle Liousse"
  ],
  "comment": "15 pages, 2 figures, references added",
  "journal": "Nonlinearity (2009), vol 22 no. 8, p 1899-1907",
  "categories": [
    "math.DS"
  ],
  "abstract": "In 1991 Llibre and MacKay proved that if $f$ is a 2-torus homeomorphism isotopic to identity and the rotation set of $f$ has a non empty interior then $f$ has positive topological entropy. Here, we give a converselike theorem. We show that the interior of the rotation set of a 2-torus $C^{1+ \\alpha}$ diffeomorphism isotopic to identity of positive topological entropy is not empty, under the additional hypotheses that $f$ is topologically transitive and irreducible. We also give examples that show that these hypotheses are necessary.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-04-25T17:43:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E45",
      "37E30"
    ],
    "keywords": [
      "rotation set",
      "positive topological entropy",
      "non empty interior",
      "homeomorphism isotopic",
      "additional hypotheses"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/22/8/007",
      "journal": "Nonlinearity",
      "year": 2009,
      "month": "Aug",
      "volume": 22,
      "number": 8,
      "pages": 1899
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009Nonli..22.1899E"
    }
  }
}