{
  "id": "1005.4828",
  "version": "v1",
  "published": "2010-05-26T14:31:26.000Z",
  "updated": "2010-05-26T14:31:26.000Z",
  "title": "The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes",
  "authors": [
    "Artur Avila",
    "Mikhail Lyubich"
  ],
  "comment": "44 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove exponential contraction of renormalization along hybrid classes of infinitely renormalizable unimodal maps (with arbitrary combinatorics), in any even degree $d$. We then conclude that orbits of renormalization are asymptotic to the full renormalization horseshoe, which we construct. Our argument for exponential contraction is based on a precompactness property of the renormalization operator (\"beau bounds\"), which is leveraged in the abstract analysis of holomorphic iteration. Besides greater generality, it yields a unified approach to all combinatorics and degrees: there is no need to account for the varied geometric details of the dynamics, which were the typical source of contraction in previous restricted proofs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-26T14:31:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "full renormalization horseshoe",
      "exponential contraction",
      "hybrid classes",
      "higher degree",
      "precompactness property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.4828A"
    }
  }
}