{
  "id": "2308.15580",
  "version": "v1",
  "published": "2023-08-29T19:12:31.000Z",
  "updated": "2023-08-29T19:12:31.000Z",
  "title": "Immediate renormalization of cubic complex polynomials with empty rational lamination",
  "authors": [
    "Alexander Blokh",
    "Lex Oversteegen",
    "Vladlen Timorin"
  ],
  "comment": "26 pages, 1 figure; accepted to a special issue of the MMJ dedicated to Yulij Ilyashenko's 80th Birthday. arXiv admin note: substantial text overlap with arXiv:2102.10325",
  "categories": [
    "math.DS"
  ],
  "abstract": "A cubic polynomial $P$ with a non-repelling fixed point $b$ is said to be immediately renormalizable if there exists a (connected) QL invariant filled Julia set $K^*$ such that $b\\in K^*$. In that case, exactly one critical point of $P$ does not belong to $K^*$. We show that if, in addition, the Julia set of $P$ has no (pre)periodic cutpoints, then this critical point is recurrent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-29T19:12:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F20",
      "37C25",
      "37F10",
      "37F50"
    ],
    "keywords": [
      "cubic complex polynomials",
      "empty rational lamination",
      "immediate renormalization",
      "ql invariant filled julia set",
      "critical point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}