{
  "id": "1506.02223",
  "version": "v1",
  "published": "2015-06-07T05:47:03.000Z",
  "updated": "2015-06-07T05:47:03.000Z",
  "title": "Renormalization of Hénon map in arbitrary dimension I : Universality and reduction of ambient space",
  "authors": [
    "Young Woo Nam"
  ],
  "comment": "42 pages, 2 figures. arXiv admin note: text overlap with arXiv:1408.4289",
  "categories": [
    "math.DS"
  ],
  "abstract": "Period doubling H\\'enon renormalization of strongly dissipative maps is generalized in arbitrary finite dimension. In particular, a small perturbation of toy model maps with dominated splitting has invariant $C^r$ surfaces embedded in higher dimension and the Cantor attractor has unbounded geometry with respect to full Lebesgue measure on the parameter space. It is an extension of dynamical properties of three dimensional infinitely renormalizable H\\'enon-like map in arbitrary finite dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-07T05:47:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F25"
    ],
    "keywords": [
      "arbitrary dimension",
      "hénon map",
      "ambient space",
      "arbitrary finite dimension",
      "infinitely renormalizable henon-like map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150602223N"
    }
  }
}