{
  "id": "math/0406004",
  "version": "v2",
  "published": "2004-05-31T22:53:47.000Z",
  "updated": "2005-12-22T17:30:48.000Z",
  "title": "A numerical method for constructing the hyperbolic structure of complex Henon mappings",
  "authors": [
    "Suzanne Lynch Hruska"
  ],
  "comment": "25 pages. 5 figures. Submitted",
  "journal": "Found. Comput. Math. 6 (2006), no. 4, 427--455.",
  "categories": [
    "math.DS"
  ],
  "abstract": "For complex parameters a,c, we consider the Henon mapping H_{a,c}: C^2 -> C^2 given by (x,y) -> (x^2 +c -ay, x), and its Julia set, J. In this paper, we describe a rigorous computer program for attempting to construct a cone field in the tangent bundle over J, which is preserved by DH, and a continuous norm in which DH (and DH^{-1}) uniformly expands the cones (and their complements). We show a consequence of a successful construction is a proof that H is hyperbolic on J. We give several new examples of hyperbolic maps, produced with our computer program, Hypatia, which implements our methods.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-12-22T17:30:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32H50",
      "37F15",
      "37C50",
      "37-04",
      "37F50"
    ],
    "keywords": [
      "complex henon mappings",
      "hyperbolic structure",
      "numerical method",
      "tangent bundle",
      "julia set"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6004L"
    }
  }
}