{
  "id": "0905.0088",
  "version": "v1",
  "published": "2009-05-01T13:16:46.000Z",
  "updated": "2009-05-01T13:16:46.000Z",
  "title": "Indices of the iterates of ({\\Bbb R}^3)-homeomorphisms at fixed points which are isolated invariant sets",
  "authors": [
    "Patrice Le Calvez",
    "Francisco R. Ruiz del Portal",
    "José M. Salazar"
  ],
  "doi": "10.1112/jlms/jdq050",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let (U \\subset {\\mathbb R}^3) be an open set and (f:U \\to f(U) \\subset {\\mathbb R}^3) be a homeomorphism. Let (p \\in U) be a fixed point. It is known that, if (\\{p\\}) is not an isolated invariant set, the sequence of the fixed point indices of the iterates of (f) at (p), ((i(f^n,p))_{n\\geq 1}), is, in general, unbounded. The main goal of this paper is to show that when (\\{p\\}) is an isolated invariant set, the sequence ((i(f^n,p))_{n\\geq 1}) is periodic. Conversely, we show that for any periodic sequence of integers ((I_n)_{n \\geq1}) satisfying Dold's necessary congruences, there exists an orientation preserving homeomorphism such that (i(f^n,p)=I_n) for every (n\\geq 1). Finally we also present an application to the study of the local structure of the stable/unstable sets at (p).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-01T13:16:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C25",
      "37B30",
      "54H25"
    ],
    "keywords": [
      "isolated invariant set",
      "fixed point",
      "satisfying dolds necessary congruences",
      "point indices",
      "main goal"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.0088L"
    }
  }
}