{
  "id": "1210.8285",
  "version": "v1",
  "published": "2012-10-31T10:20:23.000Z",
  "updated": "2012-10-31T10:20:23.000Z",
  "title": "On Poincare series of unicritical polynomials at the critical point",
  "authors": [
    "Juan Rivera-Letelier",
    "Weixiao Shen"
  ],
  "comment": "17 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we show that for a unicritical polynomial having a priori bounds, the unique conformal measure of minimal exponent has no atom at the critical point. For a conformal measure of higher exponent, we give a necessary and sufficient condition for the critical point to be an atom, in terms of the growth rate of the derivatives at the critical value.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-31T10:20:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical point",
      "unicritical polynomial",
      "poincare series",
      "unique conformal measure",
      "priori bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.8285R"
    }
  }
}