{
  "id": "1509.07558",
  "version": "v1",
  "published": "2015-09-24T22:49:52.000Z",
  "updated": "2015-09-24T22:49:52.000Z",
  "title": "The Hausdorff dimension of quasi-circles: a result of Ruelle and Bowen",
  "authors": [
    "Catherine Bruce"
  ],
  "comment": "9 pages, 2 figures, to be submitted to The American Mathematical Monthly",
  "categories": [
    "math.DS"
  ],
  "abstract": "We provide an expanded and clarified proof of the famous result of Bowen and Ruelle giving an asymptotic formula for the Hausdorff dimension of quasi-circles corresponding to the Julia sets of $f(z)=z^2+c$ for small $c$. The proof does not contain new material but has been rewritten to make it more accessible to MSc or PhD students with an interest in dimension theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-24T22:49:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C45",
      "28A80",
      "37F50"
    ],
    "keywords": [
      "hausdorff dimension",
      "quasi-circles",
      "asymptotic formula",
      "dimension theory",
      "julia sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}