{
  "id": "math/0408041",
  "version": "v5",
  "published": "2004-08-03T14:06:20.000Z",
  "updated": "2008-05-20T15:43:10.000Z",
  "title": "Siegel Disks and Periodic Rays of Entire Functions",
  "authors": [
    "Lasse Rempe"
  ],
  "comment": "22 pages, 4 figures. A problem with the image quality of some of the figures was fixed. Some minor corrections were also made. Final version",
  "journal": "J. Reine Angew. Math. 624, 81-102 (2008).",
  "doi": "10.1515/CRELLE.2008.081",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let f be an entire function whose set of singular values is bounded and suppose that f has a Siegel disk such that f restricts to a homeomorphism of the boundary. We show that the Siegel disk is bounded. Using a result of Herman, we deduce that if additionally the rotation number of the Siegel disk is Diophantine, then its boundary contains a critical point of f. Suppose furthermore that all singular values of f lie in the Julia set. We prove that, if f has a Siegel disk $U$ whose boundary contains no singular values, then the condition that f is a homeomorphism of the boundary of U is automatically satisfied. We also investigate landing properties of periodic dynamic rays by similar methods.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2008-05-20T15:43:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "30D05"
    ],
    "keywords": [
      "siegel disk",
      "entire function",
      "periodic rays",
      "singular values",
      "boundary contains"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8041R"
    }
  }
}