{
  "id": "1506.07221",
  "version": "v1",
  "published": "2015-06-24T01:58:18.000Z",
  "updated": "2015-06-24T01:58:18.000Z",
  "title": "Hénon renormalization in arbitrary dimension : Invariant space under renormalization operator",
  "authors": [
    "Young Woo Nam"
  ],
  "comment": "42 pages. arXiv admin note: substantial text overlap with arXiv:1408.4619",
  "categories": [
    "math.DS"
  ],
  "abstract": "Infinitely renormalizable H\\'enon-like map in arbitrary finite dimension is considered. The set, $\\mathcal N$ of infinitely renormalizable H\\'enon-like maps satisfying the certain condition is invariant under renormalization operator. The Cantor attractor of infinitely renormalizable H\\'enon-like map, $F$ in $\\mathcal N$ has {\\em unbounded geometry} almost everywhere in the parameter space of the universal number which corresponds to the average Jacobian of two dimensional map. This is an extension of the same result in $\\mathcal N$ for three dimensional infinitely renormalizable H\\'enon-like maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-24T01:58:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "infinitely renormalizable henon-like map",
      "renormalization operator",
      "invariant space",
      "arbitrary dimension",
      "hénon renormalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150607221N"
    }
  }
}