{
  "id": "0806.1779",
  "version": "v4",
  "published": "2008-06-11T02:15:23.000Z",
  "updated": "2008-09-16T04:13:41.000Z",
  "title": "Analytic families of holomorphic iterated function systems",
  "authors": [
    "Mario Roy",
    "Hiroki Sumi",
    "Mariusz Urbanski"
  ],
  "comment": "30 pages, the title is changed. Published in Nonlinearity 21 (2008) 2255-2279",
  "doi": "10.1088/0951-7715/21/10/004",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "This paper deals with analytic families of holomorphic iterated function systems. Using real analyticity of the pressure function (which we prove), we establish a classification theorem for analytic families of holomorphic iterated function systems which depend continuously on a parameter when the space of holomorphic iterated function systems is endowed with the \"$\\lambda$-topology\". This classification theorem allows us to generalize some geometric results from the paper (\"Lambda-Topology vs. Pointwise Topology\", to appear in Ergod. Th. & Dynam. Sys.) of the authors, and gives us a better and clearer understanding of the global structure of the space of conformal IFSs.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2008-09-16T04:13:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F35",
      "37F45"
    ],
    "keywords": [
      "holomorphic iterated function systems",
      "analytic families",
      "classification theorem",
      "paper deals",
      "conformal ifss"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Nonlinearity",
      "year": 2008,
      "month": "Oct",
      "volume": 21,
      "number": 10,
      "pages": 2255
    },
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008Nonli..21.2255R"
    }
  }
}