{
  "id": "1401.4792",
  "version": "v1",
  "published": "2014-01-20T05:43:20.000Z",
  "updated": "2014-01-20T05:43:20.000Z",
  "title": "Core entropy and biaccessibility of quadratic polynomials",
  "authors": [
    "Wolf Jung"
  ],
  "comment": "46 pages with 24 eps-figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "For complex quadratic polynomials, the topology of the Julia set and the dynamics are understood from another perspective by considering the Hausdorff dimension of biaccessing angles and the core entropy: the topological entropy on the Hubbard tree. These quantities are related according to Thurston. Tiozzo [arXiv:1305.3542] has shown continuity on principal veins of the Mandelbrot set M . This result is extended to all veins here, and it is shown that continuity with respect to the external angle theta will imply continuity in the parameter c . Level sets of the biaccessibility dimension are described, which are related to renormalization. H\\\"older asymptotics at rational angles are found, confirming the H\\\"older exponent given by Bruin--Schleicher [arXiv:1205.2544]. Partial results towards local maxima at dyadic angles are obtained as well, and a possible self-similarity of the dimension as a function of the external angle is suggested.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-20T05:43:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F20",
      "37B40",
      "37F45"
    ],
    "keywords": [
      "core entropy",
      "complex quadratic polynomials",
      "external angle theta",
      "continuity",
      "rational angles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.4792J"
    }
  }
}