{
  "id": "1011.5300",
  "version": "v1",
  "published": "2010-11-24T05:18:44.000Z",
  "updated": "2010-11-24T05:18:44.000Z",
  "title": "Ergodic Properties of Invariant Measures for C^{1+α} nonuniformly hyperbolic systems",
  "authors": [
    "Chao Liang",
    "Wenxiang Sun",
    "Xueting Tian"
  ],
  "comment": "19 pages",
  "journal": "Ergodic Theory and Dynamical Systems, 33(2), 560-584, 2013",
  "doi": "10.1017/S0143385711000940",
  "categories": [
    "math.DS"
  ],
  "abstract": "For an ergodic hyperbolic measure $\\omega$ of a $C^{1+{\\alpha}}$ diffeomorphism, there is an $\\omega$ full-measured set $\\tilde\\Lambda$ such that every nonempty, compact and connected subset $V$ of $\\mathbb{M}_{inv}(\\tilde\\Lambda)$ coincides with the accumulating set of time averages of Dirac measures supported at {\\it one orbit}, where $\\mathbb{M}_{inv}(\\tilde\\Lambda)$ denotes the space of invariant measures supported on $\\tilde\\Lambda$. Such state points corresponding to a fixed $V$ are dense in the support $supp(\\omega)$. Moreover, $\\mathbb{M}_{inv}(\\tilde\\Lambda)$ can be accumulated by time averages of Dirac measures supported at {\\it one orbit}, and such state points form a residual subset of $supp(\\omega)$. These extend results of Sigmund [9] from uniformly hyperbolic case to non-uniformly hyperbolic case. As a corollary, irregular points form a residual set of $supp(\\omega)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-24T05:18:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C40",
      "37D25",
      "37H15",
      "37A35"
    ],
    "keywords": [
      "nonuniformly hyperbolic systems",
      "invariant measures",
      "ergodic properties",
      "hyperbolic case",
      "dirac measures"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.5300L"
    }
  }
}