{
  "id": "1406.5833",
  "version": "v1",
  "published": "2014-06-23T09:05:03.000Z",
  "updated": "2014-06-23T09:05:03.000Z",
  "title": "On \"observable\" Li-Yorke tuples for interval maps",
  "authors": [
    "Henk Bruin",
    "Piotr Oprocha"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we study the set of Li-Yorke $d$-tuples and its $d$-dimensional Lebesgue measure for interval maps $T\\colon [0,1] \\to [0,1]$. If a topologically mixing $T$ preserves an absolutely continuous probability measure 9with respect to Lebesgue), then the $d$-tuples have Lebesgue full measure, but if $T$ preserves an infinite absolutely continuous measure, the situation becomes more interesting. Taking the family of Manneville-Pomeau maps as example, we show that for any $d \\ge 2$, it is possible that the set of Li-Yorke $d$-tuples has full Lebesgue measure, but the set of Li-Yorke $d+1$-tuples has zero Lebesgue measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-23T09:05:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E05"
    ],
    "keywords": [
      "interval maps",
      "li-yorke tuples",
      "continuous probability measure 9with respect",
      "lebesgue full measure",
      "absolutely continuous probability measure 9with"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/28/6/1675",
      "journal": "Nonlinearity",
      "year": 2015,
      "month": "Jun",
      "volume": 28,
      "number": 6,
      "pages": 1675
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015Nonli..28.1675B"
    }
  }
}