{
  "id": "1202.2282",
  "version": "v4",
  "published": "2012-02-10T15:27:25.000Z",
  "updated": "2016-07-12T11:26:12.000Z",
  "title": "Typical orbits of quadratic polynomials with a neutral fixed point: Brjuno type",
  "authors": [
    "Davoud Cheraghi"
  ],
  "comment": "38 pages, 5 figures; fixed the issues with processing the figures",
  "journal": "Comm Math Phys 322 (2013), No 3",
  "doi": "10.1007/s00220-013-1747-5",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "We describe the topological behavior of typical orbits of complex quadratic polynomials P_alpha(z)=e^{2\\pi i alpha} z+z^2, with alpha of high return type. Here we prove that for such Brjuno values of alpha the closure of the critical orbit, which is the measure theoretic attractor of the map, has zero area. Then combining with Part I of this work, we show that the limit set of the orbit of a typical point in the Julia set is equal to the closure of the critical orbit.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-11-16T23:27:13.000Z",
      "comment": "38 pages, 5 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2016-07-12T11:26:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F50",
      "58F12"
    ],
    "keywords": [
      "neutral fixed point",
      "typical orbits",
      "brjuno type",
      "complex quadratic polynomials",
      "high return type"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00220-013-1747-5",
      "journal": "Commun. Math. Phys.",
      "year": 2013,
      "month": "Sep",
      "volume": 322,
      "number": 3,
      "pages": 999,
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013CMaPh.322..999C"
    }
  }
}