{
  "id": "1501.05488",
  "version": "v1",
  "published": "2015-01-22T13:07:55.000Z",
  "updated": "2015-01-22T13:07:55.000Z",
  "title": "Connectivity of Julia sets of Newton maps: A unified approach",
  "authors": [
    "Krzysztof Barański",
    "Núria Fagella",
    "Xavier Jarque",
    "Bogusława Karpińska"
  ],
  "comment": "15 pages, 3 figures. arXiv admin note: text overlap with arXiv:1206.6667",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we give a unified proof of the fact that the Julia set of Newton's method applied to a holomorphic function of the complex plane (a polynomial of degree large than $1$ or an entire transcendental function) is connected. The result was recently completed by the authors' previous work, as a consequence of a more general theorem whose proof spreads among many papers, which consider separately a number of particular cases for rational and transcendental maps, and use a variety of techniques. In this note we present a unified, direct and reasonably self-contained proof which works for all situations alike.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-22T13:07:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30D05",
      "37F10",
      "30D30"
    ],
    "keywords": [
      "julia set",
      "newton maps",
      "unified approach",
      "connectivity",
      "entire transcendental function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150105488B"
    }
  }
}