{
  "id": "1211.0600",
  "version": "v2",
  "published": "2012-11-03T06:33:14.000Z",
  "updated": "2015-01-07T11:36:22.000Z",
  "title": "Herman rings of meromorphic maps with an omitted value",
  "authors": [
    "Tarakanta Nayak"
  ],
  "comment": "12 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We investigate the existence and distribution of Herman rings of transcendental meromorphic functions which have at least one omitted value. If all the poles of such a function are multiple then it has no Herman ring. Herman rings of period one or two do not exist. Functions with a single pole or with at least two poles one of which is an omitted value have no Herman ring. Every doubly connected periodic Fatou component is a Herman ring.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-03T06:33:14.000Z",
      "abstract": "Following are proved on Herman rings of meromorphic functions having at least one omitted value. If all the poles of such a function are multiple then it has no Herman ring. Herman ring of period one or two does not exist. Functions with a single pole or with at least two poles one of which is an omitted value have no Herman ring. Every doubly connected periodic Fatou component is a Herman ring.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-07T11:36:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "37F45"
    ],
    "keywords": [
      "herman ring",
      "omitted value",
      "meromorphic maps",
      "doubly connected periodic fatou component",
      "meromorphic functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.0600N"
    }
  }
}