{
  "id": "1402.7327",
  "version": "v5",
  "published": "2014-02-28T17:29:48.000Z",
  "updated": "2015-09-15T01:36:25.000Z",
  "title": "Weak forms of topological and measure theoretical equicontinuity: relationships with discrete spectrum and sequence entropy",
  "authors": [
    "Felipe García-Ramos"
  ],
  "comment": "To appear in Ergodic theory and dynamical systems",
  "categories": [
    "math.DS"
  ],
  "abstract": "We define weaker forms of topological and measure theoretical equicontinuity for topological dynamical systems and we study their relationships with systems with discrete spectrum and zero sequence entropy. In the topological category we show systems with zero topological sequence entropy are strictly contained in the diam-mean equicontinuous systems; and that transitive almost automorphic subshifts are diam-mean equicontinuous if and only if they are regular (i.e. the maximal equicontinuous factor map is 1-1 on a set of full Haar measure). In the measure category we show that for ergodic topological systems having discrete spectrum is equivalent of being {\\mu}-mean equicontinuous. For both categories we find characterizations using stronger versions of the classical notion of sensitivity.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-07-03T19:21:31.000Z",
      "abstract": "We define weaker forms of topological and measure theoretical equicontinuity for topological dynamical systems and we study their relationships with systems with discrete spectrum and zero sequence entropy. In the topological category we show systems with zero topological sequence entropy are strictly contained in the weakly equicontinuous systems; and that transitive almost automorphic subshifts are weakly equicontinuous if and only if they are regular (i.e. the maximal equicontinuous factor map is 1-1 on a set of full Haar measure). In the measure category we show that for ergodic topological systems having discrete spectrum is equivalent of being {\\mu}-very weakly equicontinuous. For both categories we find characterizations using stronger versions of the classical notion of sensitivity.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v5",
      "updated": "2015-09-15T01:36:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "37B10",
      "37B40",
      "37A05",
      "37A30",
      "37A35"
    ],
    "keywords": [
      "measure theoretical equicontinuity",
      "discrete spectrum",
      "weak forms",
      "relationships",
      "define weaker forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.7327G"
    }
  }
}