{
  "id": "1312.0292",
  "version": "v3",
  "published": "2013-12-02T00:26:04.000Z",
  "updated": "2015-11-19T08:20:22.000Z",
  "title": "Ergodic properties of invariant measures for systems with average shadowing property",
  "authors": [
    "Yiwei Dong",
    "Xueting Tian",
    "Xiaoping Yuan"
  ],
  "comment": "average shadowing may be not enough for results in this paper, we replaced average shadowing by asymptotic average shadowing. see the paper \" Ergodic properties of systems with asymptotic average shadowing property, Journal of Mathematical Analysis and Applications, 2015, Vol. 432(1), 53-73.\"",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we explore a topological system $f:M\\rightarrow M$ with average shadowing property. We extend Sigmund's results and show that every non-empty, compact and connected subset $V\\subseteq\\mathcal {M}_{inv}(f)$ coincides with $V_f(y)$, where $\\mathcal {M}_{inv}(f)$ denotes the space of invariant Borel probability measures on M, and $V_f(y)$ denotes the accumulation set of time average of Dirac measures supported at the orbit of $y$. We also show that the set $M_{V}=\\{y\\in M\\,\\,|\\,\\,V_{f}(y)=V\\}$ is dense in $\\Delta_{V}=\\bigcup_{\\nu\\in V}supp(\\nu)$. In particular, if $\\Delta_{max}=\\bigcup_{\\nu\\in\\mathcal {M}_{inv}(f)}supp(\\nu)$ is isolated or coincides with $M$, then $M_{max}=\\{y: V_{f}(y)=\\mathcal {M}_{inv}(f)\\}$ is residual in $\\Delta_{max}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-30T07:39:03.000Z",
      "comment": "18pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-11-19T08:20:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "average shadowing property",
      "ergodic properties",
      "invariant measures",
      "invariant borel probability measures",
      "extend sigmunds results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.0292D"
    }
  }
}