{
  "id": "2010.15386",
  "version": "v1",
  "published": "2020-10-29T06:51:54.000Z",
  "updated": "2020-10-29T06:51:54.000Z",
  "title": "Rays to renormalizations",
  "authors": [
    "Genadi Levin"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let P be a non-linear polynomial, K_P the filled Julia set of P, f a renormalization of P and K_f the filled Julia set of f. We show, loosely speaking, that there is a finite-to-one function \\lambda from the set of P-external rays having limit points in K_f onto the set of f-external rays to K_f such that R and \\lambda(R) share the same limit set. In particular, if a point of the Julia set J_f=\\partial K_f of a renormalization is accessible from C\\setminus K_f then it is accessible through an external ray of P (the inverse is obvious). Another interesting corollary is that: a component of K_P\\setminus K_f can meet K_f only at a single (pre-)periodic point. We study also a correspondence induced by \\lambda on arguments of rays. These results are generalizations to all polynomials (covering notably the case of connected Julia set K_P) of some results of Levin-Przytycki, Blokh-Childers-Levin-Oversteegen-Schleicher and Petersen-Zakeri where the case is considered when K_P is disconnected and K_f is a periodic component of K_P.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-29T06:51:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "renormalization",
      "filled julia set",
      "connected julia set",
      "finite-to-one function",
      "p-external rays"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}