{
  "id": "0704.2978",
  "version": "v1",
  "published": "2007-04-23T11:42:25.000Z",
  "updated": "2007-04-23T11:42:25.000Z",
  "title": "On Loops in the Hyperbolic Locus of the Complex Hénon Map and Their Monodromies",
  "authors": [
    "Zin Arai"
  ],
  "comment": "17 pages, 9 figures. For supplemental materials, see http://www.math.kyoto-u.ac.jp/~arai/",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove John Hubbard's conjecture on the topological complexity of the hyperbolic horseshoe locus of the complex H\\'enon map. Indeed, we show that there exist several non-trivial loops in the locus which generate infinitely many mutually different monodromies. Our main tool is a rigorous computational algorithm for verifying the uniform hyperbolicity of chain recurrent sets. In addition, we show that the dynamics of the real H\\'enon map is completely determined by the monodromy of a certain loop, providing the parameter of the map is contained in the hyperbolic horseshoe locus of the complex H\\'enon map.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-04-23T11:42:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F45",
      "37B10",
      "37D20",
      "58K10"
    ],
    "keywords": [
      "complex hénon map",
      "hyperbolic locus",
      "complex henon map",
      "hyperbolic horseshoe locus",
      "real henon map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.2978A"
    }
  }
}