{
  "id": "0908.0574",
  "version": "v2",
  "published": "2009-08-05T02:06:36.000Z",
  "updated": "2010-11-10T06:34:58.000Z",
  "title": "Family-independence for topological and measurable dynamics",
  "authors": [
    "Wen Huang",
    "Hanfeng Li",
    "Xiangdong Ye"
  ],
  "comment": "Minor change. To appear in Trans. Amer. Math. Soc",
  "journal": "Trans. Amer. Math. Soc. 364 (2012), no. 10, 5209--5245",
  "categories": [
    "math.DS"
  ],
  "abstract": "For a family F (a collection of subsets of Z_+), the notion of F-independence is defined both for topological dynamics (t.d.s.) and measurable dynamics (m.d.s.). It is shown that there is no non-trivial {syndetic}-independent m.d.s.; a m.d.s. is {positive-density}-independent if and only if it has completely positive entropy; and a m.d.s. is weakly mixing if and only if it is {IP}-independent. For a t.d.s. it is proved that there is no non-trivial minimal {syndetic}-independent system; a t.d.s. is weakly mixing if and only if it is {IP}-independent. Moreover, a non-trivial proximal topological K system is constructed, and a topological proof of the fact that minimal topological K implies strong mixing is presented.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-11-10T06:34:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B40",
      "37A35",
      "37B10",
      "37A05"
    ],
    "keywords": [
      "measurable dynamics",
      "family-independence",
      "non-trivial minimal",
      "implies strong",
      "positive entropy"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.0574H"
    }
  }
}