{
  "id": "math/0609045",
  "version": "v3",
  "published": "2006-09-01T21:59:29.000Z",
  "updated": "2023-12-28T23:51:18.000Z",
  "title": "A priori bounds for some infinitely renormalizable quadratics: I. Bounded primitive combinatorics",
  "authors": [
    "Jeremy Kahn"
  ],
  "comment": "LaTeX, 63 pages, 5 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove the a priori bounds for infinitely renormalizable quadratic polynomials for which we can find an infinite sequence of primitive renormalizations such that the ratios of the periods of successive renormalizations is bounded. This implies the local connectivity of the Mandelbrot set at the corresponding points.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-09-06T19:10:00.000Z",
      "abstract": "We prove the a priori bounds for infinitely renormalizable quadratic polynomials of bounded primitive type. This implies the local connectivity of the Mandelbrot set at the corresponding points.",
      "comment": "LaTeX, 39 pages, 1 figure",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2023-12-28T23:51:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F25",
      "37F45"
    ],
    "keywords": [
      "bounded primitive combinatorics",
      "priori bounds",
      "infinitely renormalizable quadratic polynomials",
      "mandelbrot set",
      "local connectivity"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 63,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9045K"
    }
  }
}