{
  "id": "1211.4535",
  "version": "v3",
  "published": "2012-11-19T18:53:51.000Z",
  "updated": "2014-07-29T09:34:51.000Z",
  "title": "Singular values and bounded Siegel disks",
  "authors": [
    "Anna Miriam Benini",
    "Nuria Fagella"
  ],
  "comment": "Minor changes in the arguments, improved exposition. Same results",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $f$ be an entire transcendental function of finite order and $\\Delta$ be a forward invariant bounded Siegel disk for $f$ with rotation number in Herman's class $\\mathcal{H}$. We show that if $f$ has two singular values with bounded orbit, then the boundary of $\\Delta$ contains a critical point. We also give a criterion under which the critical point in question is recurrent. We actually prove a more general theorem with less restrictive hypotheses, from which these results follow.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-07-29T09:34:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "37F20",
      "37F50"
    ],
    "keywords": [
      "singular values",
      "entire transcendental function",
      "forward invariant bounded siegel disk",
      "critical point",
      "general theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.4535B"
    }
  }
}