{
  "id": "math/9608213",
  "version": "v1",
  "published": "1996-08-15T00:00:00.000Z",
  "updated": "1996-08-15T00:00:00.000Z",
  "title": "Geography of the cubic connectedness locus I: Intertwining surgery",
  "authors": [
    "Adam L. Epstein",
    "Michael Yampolsky"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We exhibit products of Mandelbrot sets in the two-dimensional complex parameter space of cubic polynomials. These products were observed by J. Milnor in computer experiments which inspired Lavaurs' proof of non local-connectivity for the cubic connectedness locus. Cubic polynomials in such a product may be renormalized to produce a pair of quadratic maps. The inverse construction is an {\\it intertwining surgery} on two quadratics. The idea of intertwining first appeared in a collection of problems edited by Bielefeld. Using quasiconformal surgery techniques of Branner and Douady, we show that any two quadratics may be intertwined to obtain a cubic polynomial. The proof of continuity in our two-parameter setting requires further considerations involving ray combinatorics and a pullback argument.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1996-08-15T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cubic connectedness locus",
      "intertwining surgery",
      "cubic polynomial",
      "two-dimensional complex parameter space",
      "quasiconformal surgery techniques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1996math......8213E"
    }
  }
}