{
  "id": "1405.0224",
  "version": "v3",
  "published": "2014-05-01T17:18:29.000Z",
  "updated": "2014-10-22T09:12:49.000Z",
  "title": "Semigroups of transcendental entire functions and their dynamics",
  "authors": [
    "Dinesh Kumar",
    "Sanjay Kumar"
  ],
  "comment": "11 pages, work in progress. Comments are welcome. arXiv admin note: text overlap with arXiv:1401.0425",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the dynamics of an arbitrary semigroup of transcendental entire functions using Fatou-Julia theory. Several results of the dynamics associated with iteration of a transcendental entire function have been extended to transcendental semigroups. We provide some conditions for connectivity of the Julia set of the transcendental semigroups. We also study finitely generated transcendental semigroups, abelian transcendental semigroups and limit functions of transcendental semigroups on its invariant Fatou components.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-11T16:23:06.000Z",
      "comment": "12 pages, work in progress. Comments are welcome. arXiv admin note: text overlap with arXiv:1401.0425, arXiv:1302.7249",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-10-22T09:12:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "30D05"
    ],
    "keywords": [
      "transcendental entire function",
      "abelian transcendental semigroups",
      "invariant fatou components",
      "study finitely generated transcendental semigroups",
      "fatou-julia theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.0224K"
    }
  }
}