{
  "id": "1903.12640",
  "version": "v1",
  "published": "2019-03-29T17:41:20.000Z",
  "updated": "2019-03-29T17:41:20.000Z",
  "title": "When points are equivalent in long time behaviors",
  "authors": [
    "Liqi Zheng",
    "Zuohuan Zheng"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We metric the distance between two points in a new way, and then show a new equivalent condition of ergodic measures. We also conclude a necessary and sufficient condition of uniquely ergodicity. What's more, an equivalent condition of when the time average operator maps continuous functions to be continuous is shown.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-29T17:41:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "long time behaviors",
      "average operator maps continuous functions",
      "equivalent condition",
      "time average operator maps continuous"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}