{
  "id": "1504.07520",
  "version": "v1",
  "published": "2015-04-28T15:09:57.000Z",
  "updated": "2015-04-28T15:09:57.000Z",
  "title": "Positive topological entropy and $Δ$-weakly mixing sets",
  "authors": [
    "Wen Huang",
    "Jian Li",
    "Xiangdong Ye",
    "Xiaoyao Zhou"
  ],
  "comment": "26 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "The notion of $\\Delta$-weakly mixing set is introduced, which shares similar properties of weakly mixing sets. It is shown that if a dynamical system has positive topological entropy, then the collection of $\\Delta$-weakly mixing sets is residual in the closure of the collection of entropy sets in the hyperspace. The existence of $\\Delta$-weakly mixing sets in a topological dynamical system admitting an ergodic invariant measure which is not measurable distal is obtained. Moreover, Our results generalize several well known results and also answer several open questions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-28T15:09:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "37B40",
      "37A35"
    ],
    "keywords": [
      "weakly mixing set",
      "positive topological entropy",
      "shares similar properties",
      "ergodic invariant measure",
      "dynamical system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150407520H"
    }
  }
}