{
  "id": "1509.07843",
  "version": "v1",
  "published": "2015-09-25T19:25:52.000Z",
  "updated": "2015-09-25T19:25:52.000Z",
  "title": "Satellite renormalization of quadratic polynomials",
  "authors": [
    "Davoud Cheraghi",
    "Mitsuhiro Shishikura"
  ],
  "comment": "71 pages, comments welcome",
  "categories": [
    "math.DS",
    "math.CV",
    "math.SP"
  ],
  "abstract": "We prove the uniform hyperbolicity of the near-parabolic renormalization operators acting on an infinite-dimensional space of holomorphic transformations. This implies the universality of the scaling laws, conjectured by physicists in the 70's, for a combinatorial class of bifurcations. Through near-parabolic renormalizations the polynomial-like renormalizations of satellite type are successfully studied here for the first time, and new techniques are introduced to analyze the fine-scale dynamical features of maps with such infinite renormalization structures. In particular, we confirm the rigidity conjecture under a quadratic growth condition on the combinatorics. The class of maps addressed in the paper includes infinitely-renormalizable maps with degenerating geometries at small scales (lack of a priori bounds).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-25T19:25:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quadratic polynomials",
      "satellite renormalization",
      "quadratic growth condition",
      "infinite renormalization structures",
      "infinite-dimensional space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 71,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}