{
  "id": "0808.3811",
  "version": "v2",
  "published": "2008-08-28T01:32:45.000Z",
  "updated": "2008-08-31T15:18:35.000Z",
  "title": "Some Characterizations of Domination",
  "authors": [
    "Jairo Bochi",
    "Nicolas Gourmelon"
  ],
  "comment": "10 pages, 2 figures; acknowledgements added",
  "journal": "Mathematische Zeitschrift, 263, no. 1 (2009), 221-231",
  "doi": "10.1215/00127094-2008-065",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that a cocycle has a dominated splitting if and only if there is a uniform exponential gap between singular values of its iterates. Then we consider sets $\\Sigma$ in $GL(d,\\mathbb{R})$ with the property that any cocycle with values in $\\Sigma$ has a dominated splitting. We characterize these sets in terms of existence of invariant multicones, thus extending a 2-dimensional result by Avila, Bochi, and Yoccoz. We give an example showing how these multicones can fail to have convexity properties.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-08-31T15:18:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "characterizations",
      "domination",
      "uniform exponential gap",
      "invariant multicones",
      "convexity properties"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.3811B"
    }
  }
}