{
  "id": "2307.16682",
  "version": "v1",
  "published": "2023-07-31T13:58:05.000Z",
  "updated": "2023-07-31T13:58:05.000Z",
  "title": "Wandering domains with nearly bounded orbits",
  "authors": [
    "Leticia Pardo-Simón",
    "David J. Sixsmith"
  ],
  "comment": "13 pages, 2 figures",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "A major open question in transcendental dynamics asks if it is possible for points in a wandering domain to have bounded orbits, and more strongly, for a wandering domain to iterate only in a bounded domain. In this paper we give a partial answer to this question, by constructing a bounded wandering domain that spends, in a precise sense, nearly all of its time iterating in a bounded domain. This is in strong contrast to all previously known examples of wandering domains.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-31T13:58:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded orbits",
      "bounded domain",
      "major open question",
      "transcendental dynamics asks",
      "partial answer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}