{
  "id": "math/0406003",
  "version": "v2",
  "published": "2004-05-31T22:29:09.000Z",
  "updated": "2004-07-22T05:05:02.000Z",
  "title": "Constructing an expanding metric for dynamical systems in one complex variable",
  "authors": [
    "Suzanne Lynch Hruska"
  ],
  "comment": "18 pages. 8 figures. Revised version (intro. restructured, some minor clarifications through rest)",
  "journal": "Nonlinearity 18 (2005) 81-100",
  "doi": "10.1088/0951-7715/18/1/005",
  "categories": [
    "math.DS"
  ],
  "abstract": "We describe a rigorous computer algorithm for attempting to construct an explicit, discretized metric for which a complex polynomial map is expansive on a given neighborhood of its Julia set. We show construction of such a metric proves the map is hyperbolic. We also examine the question of whether the algorithm can be improved, and the related question of how to build a metric as close to euclidean as possible. Finally, we give several examples generated with our implementation of this algorithm.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-07-22T05:05:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F15",
      "37F10",
      "37F50",
      "37B35",
      "37-04"
    ],
    "keywords": [
      "dynamical systems",
      "expanding metric",
      "complex variable",
      "complex polynomial map",
      "julia set"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Nonlinearity",
      "year": 2005,
      "month": "Jan",
      "volume": 18,
      "number": 1,
      "pages": 81
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005Nonli..18...81L"
    }
  }
}