{
  "id": "1206.4707",
  "version": "v1",
  "published": "2012-06-20T20:13:14.000Z",
  "updated": "2012-06-20T20:13:14.000Z",
  "title": "Prime ends rotation numbers and periodic points",
  "authors": [
    "Andres Koropecki",
    "Patrice Le Calvez",
    "Meysam Nassiri"
  ],
  "comment": "50 pages, 15 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the problem of existence of a periodic point in the boundary of an invariant domain for a surface homeomorphism. In the area-preserving setting, a complete classification is given in terms of rationality of Carath\\'eordory's prime ends rotation number, similar to Poincar\\'e's theory for circle homeomorphisms. In particular, we prove the converse of a classic result of Cartwright and Littlewood. This has a number of consequences for generic area preserving surface diffeomorphisms. For instance, we extend previous results of J. Mather on the boundary of invariant open sets for $C^r$-generic area preserving diffeomorphisms. Most results are proved in a general context, for homeomorphisms of arbitrary surfaces with a weak nonwandering-type hypothesis. This allows us to prove a conjecture of R. Walker about co-basin boundaries, and it also has applications in holomorphic dynamics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-20T20:13:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E30",
      "37E45",
      "37B45",
      "30D40"
    ],
    "keywords": [
      "periodic point",
      "caratheordorys prime ends rotation number",
      "generic area preserving surface diffeomorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.4707K"
    }
  }
}