{
  "id": "2301.00662",
  "version": "v1",
  "published": "2023-01-02T13:34:18.000Z",
  "updated": "2023-01-02T13:34:18.000Z",
  "title": "Meromorphic functions whose action on their Julia sets is non-ergodic",
  "authors": [
    "Tao Chen",
    "Yunping Jiang",
    "Linda Keen"
  ],
  "comment": "5 figures",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "We study transcendental meromorphic functions having two prepole asymptotic values and no critical values. We prove that these functions acting on their Julia sets are non-ergodic, which illustrates the antithesis of the Keen-Kotus result in [KK2] on the ergodicity of another subfamily of functions with two asymptotic values and no critical values.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-02T13:34:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "30F05",
      "30D05",
      "37A30"
    ],
    "keywords": [
      "julia sets",
      "non-ergodic",
      "study transcendental meromorphic functions",
      "critical values",
      "prepole asymptotic values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}