{
  "id": "1312.7663",
  "version": "v3",
  "published": "2013-12-30T09:31:56.000Z",
  "updated": "2014-04-08T12:25:09.000Z",
  "title": "Mean equicontinuity and mean sensitivity",
  "authors": [
    "Jian Li",
    "Siming Tu",
    "Xiangdong Ye"
  ],
  "comment": "25 pages, changes suggested by the referee incorporated, to appear in Ergodic Theory and Dynamical Systems",
  "doi": "10.1017/etds.2014.41",
  "categories": [
    "math.DS"
  ],
  "abstract": "Answering an open question affirmatively it is shown that every ergodic invariant measure of a mean equicontinuous (i.e. mean-L-stable) system has discrete spectrum. Dichotomy results related to mean equicontinuity and mean sensitivity are obtained when a dynamical system is transitive or minimal. Localizing the notion of mean equicontinuity, notions of almost mean equicontinuity and almost Banach mean equicontinuity are introduced. It turns out that a system with the former property may have positive entropy and meanwhile a system with the later property must have zero entropy.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-04-08T12:25:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H20",
      "37B25",
      "37B05",
      "37B40"
    ],
    "keywords": [
      "mean sensitivity",
      "banach mean equicontinuity",
      "ergodic invariant measure",
      "zero entropy",
      "open question"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.7663L"
    }
  }
}