{
  "id": "1712.00273",
  "version": "v1",
  "published": "2017-12-01T11:09:13.000Z",
  "updated": "2017-12-01T11:09:13.000Z",
  "title": "Singular values and non-repelling cycles for entire transcendental maps",
  "authors": [
    "Anna Miriam Benini",
    "Núria Fagella"
  ],
  "comment": "13 pages, 1 figure",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $f$ be a map with bounded set of singular values for which periodic dynamic rays exist and land. We prove that each non-repelling cycle is associated to a singular orbit which cannot accumulate on any other non-repelling cycle. When $f$ has finitely many singular values this implies a refinement of the Fatou-Shishikura inequality. Our approach is combinatorial in the spirit of the approach used by [Ki00], [BCL+16] for polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-01T11:09:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30D05",
      "37F10",
      "30D30"
    ],
    "keywords": [
      "entire transcendental maps",
      "singular values",
      "non-repelling cycle",
      "periodic dynamic rays",
      "singular orbit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}