{
  "id": "1211.4505",
  "version": "v2",
  "published": "2012-11-19T17:14:25.000Z",
  "updated": "2014-09-21T22:12:39.000Z",
  "title": "Statistical properties of quadratic polynomials with a neutral fixed point",
  "authors": [
    "Artur Avila",
    "Davoud Cheraghi"
  ],
  "comment": "55 pages; Substantial revisions have been made to the previous version",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "We describe the statistical properties of the dynamics of the quadratic polynomials P_a(z):=e^{2\\pi a i} z+z^2 on the complex plane, with a of high return times. In particular, we show that these maps are uniquely ergodic on their measure theoretic attractors, and the unique invariant probability is a physical measure describing the statistical behavior of typical orbits in the Julia set. This confirms a conjecture of Perez-Marco on the unique ergodicity of hedgehog dynamics, in this class of maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-19T17:14:25.000Z",
      "abstract": "We describe the statistical properties of the dynamics of the maps P_a(z):=e^{2\\pi a i} z+z^2, with a of high return times. In particular, we show that these maps are uniquely ergodic on their measure theoretic attractors, and the unique invariant probability describes the statistical behavior of typical orbits in the Julia set. In particular, this confirms the conjecture of Perez-Marco on the unique ergodicity of hedgehog dynamics, in this class of maps.",
      "comment": "24 pages, 3 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-21T22:12:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F50",
      "58F11",
      "37F25"
    ],
    "keywords": [
      "neutral fixed point",
      "statistical properties",
      "quadratic polynomials",
      "unique invariant probability",
      "measure theoretic attractors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.4505A"
    }
  }
}