{
  "id": "0809.0379",
  "version": "v3",
  "published": "2008-09-02T12:26:05.000Z",
  "updated": "2010-04-13T16:18:06.000Z",
  "title": "Multipliers of periodic orbits in spaces of rational maps",
  "authors": [
    "Genadi Levin"
  ],
  "comment": "Final version. To appear in ETDS",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "Given a polynomial or a rational map f we associate to it a space of maps. We introduce local coordinates in this space, which are essentially the set of critical values of the map. Then we consider an arbitrary periodic orbit of f with multiplier \\rho\\not=1 as a function of the local coordinates, and establish a simple connection between the dynamical plane of f and the function \\rho in the space associated to f. The proof is based on the theory of quasiconformal deformations of rational maps. As a corollary, we show that multipliers of non-repelling periodic orbits are also local coordinates in the space.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-04-13T16:18:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "37C30",
      "37F45",
      "30D05"
    ],
    "keywords": [
      "rational map",
      "multiplier",
      "local coordinates",
      "arbitrary periodic orbit",
      "non-repelling periodic orbits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.0379L"
    }
  }
}