{
  "id": "0910.5278",
  "version": "v1",
  "published": "2009-10-28T02:13:29.000Z",
  "updated": "2009-10-28T02:13:29.000Z",
  "title": "On the geometry of Julia sets",
  "authors": [
    "O. Costin",
    "M. Huang"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that the Julia set of quadratic maps with parameters in hyperbolic components of the Mandelbrot set is given by a transseries formula, rapidly convergent at any repelling periodic point. Up to conformal transformations, we obtain $J$ from a smoother curve of lower Hausdorff dimension, by replacing pieces of the more regular curve by increasingly rescaled elementary \"bricks\" obtained from the transseries expression. Self-similarity of $J$, up to conformal transformation, is manifest in the formulas. The Hausdorff dimension of $J$ is estimated by the transseries formula. The analysis extends to polynomial maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-28T02:13:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "37F45",
      "37F50",
      "30D05",
      "28A80"
    ],
    "keywords": [
      "julia set",
      "conformal transformation",
      "transseries formula",
      "lower hausdorff dimension",
      "transseries expression"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.5278C"
    }
  }
}