{
  "id": "1105.5598",
  "version": "v2",
  "published": "2011-05-27T16:00:57.000Z",
  "updated": "2011-06-03T21:17:28.000Z",
  "title": "The Schwarzian derivative and polynomial iteration",
  "authors": [
    "Hexi Ye"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the Schwarzian derivative $S_f$ of a complex polynomial $f$ and its iterates. We show that the sequence $S_{f^n}/d^{2n}$ converges to $-2(\\partial G_f)^2$, for $G_f$ the escape-rate function of $f$. As a quadratic differential, the Schwarzian derivative $S_{f^n}$ determines a conformal metric on the plane. We study the ultralimit of these metric spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-06-03T21:17:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schwarzian derivative",
      "polynomial iteration",
      "metric spaces",
      "complex polynomial",
      "quadratic differential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.5598Y"
    }
  }
}