{
  "id": "math/0104103",
  "version": "v2",
  "published": "2001-04-09T17:02:42.000Z",
  "updated": "2001-11-06T09:38:01.000Z",
  "title": "A formula with some applications to the theory of Lyapunov exponents",
  "authors": [
    "Artur Avila",
    "Jairo Bochi"
  ],
  "comment": "11 pages, no figures, final version, accepted by the Israel Journal of Mathematics",
  "journal": "Israel Journal of Mathematics, 131 (2002), 125-137.",
  "doi": "10.1007/BF02785853",
  "categories": [
    "math.DS",
    "math.RA"
  ],
  "abstract": "We prove an elementary formula about the average expansion of certain products of 2 by 2 matrices. This permits us to quickly re-obtain an inequality by M. Herman and a theorem by Dedieu and Shub, both concerning Lyapunov exponents. Indeed, we show that equality holds in Herman's result. Finally, we give a result about the growth of the spectral radius of products.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-11-06T09:38:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34D08",
      "15A04"
    ],
    "keywords": [
      "applications",
      "average expansion",
      "spectral radius",
      "elementary formula",
      "concerning lyapunov exponents"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Commun. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......4103A"
    }
  }
}