{
  "id": "1204.0250",
  "version": "v1",
  "published": "2012-04-01T18:04:44.000Z",
  "updated": "2012-04-01T18:04:44.000Z",
  "title": "Exponential growth of norms in semigroups of linear automorphisms and Hausdorff dimension of self-projective IFS",
  "authors": [
    "Roberto De Leo"
  ],
  "comment": "66 pages, 7 figures, 3 tables",
  "categories": [
    "math.DS",
    "nlin.CD"
  ],
  "abstract": "Given a finitely generated semigroup S of the (normed) set of linear maps of a vector space V into itself, we find sufficient conditions for the exponential growth of the number N(k) of elements of the semigroup contained in the sphere of radius k as k->infinity. We relate the growth rate lim log N(k)/log k to the exponent of a zeta function naturally defined on the semigroup and, in case S is a semigroup of volume-preserving automorpisms, to the Hausdorff and box dimensions of the limit set of the induced semigroup of automorphisms on the corresponding projective space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-01T18:04:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C30",
      "47D03",
      "47H20",
      "53A20"
    ],
    "keywords": [
      "exponential growth",
      "linear automorphisms",
      "hausdorff dimension",
      "self-projective ifs",
      "growth rate lim log"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 66,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.0250D"
    }
  }
}