{
  "id": "1510.08703",
  "version": "v1",
  "published": "2015-10-29T14:19:47.000Z",
  "updated": "2015-10-29T14:19:47.000Z",
  "title": "Ergodicity: from another point of view",
  "authors": [
    "Aliasghar Sarizadeh"
  ],
  "comment": "11 page",
  "categories": [
    "math.DS"
  ],
  "abstract": "In the present work, we study iterated function systems (IFSs) and their induced IFSs. We introduce a weaker concept of minimality for induced IFSs so that this property together whit $C^1$-regularity of generators implies that the Lebesgue measure is ergodic for our original IFS. As a consequence of mentioned results, we obtain $C^1$-ergodicity for some cascade systems. Moreover, we also obtain that the Lebesgue measure is ergodic for a dense subset of the space $\\overline{\\mathcal{O}}^\\infty(\\mathbb{T}^2)$ where $\\overline{\\mathcal{O}}^\\infty(\\mathbb{T}^2)$ is the $C^\\infty$-closure of the conjugancy class of translations of $\\mathbb{T}^2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-29T14:19:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ergodicity",
      "lebesgue measure",
      "study iterated function systems",
      "induced ifss",
      "weaker concept"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}