{
  "id": "1004.3439",
  "version": "v1",
  "published": "2010-04-20T13:15:27.000Z",
  "updated": "2010-04-20T13:15:27.000Z",
  "title": "The Structure on Invariant Measures of $C^1$ generic diffeomorphisms",
  "authors": [
    "Wenxiang Sun",
    "Xueting Tian"
  ],
  "journal": "Acta Mathematica Sinica, English Series, 2012 Volume 28, Number 4, 817-824",
  "doi": "10.1007/s10114-011-9723-5",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $\\Lambda$ be an isolated non-trival transitive set of a $C^1$ generic diffeomorphism $f\\in\\Diff(M)$. We show that the space of invariant measures supported on $\\Lambda$ coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in $\\Lambda$ (which implies the set of irregular$^+$ points is also residual in $\\Lambda$). As an application, we show that the non-uniform hyperbolicity of irregular$^+$ points in $\\Lambda$ with totally 0 measure (resp., the non-uniform hyperbolicity of a generic subset in $\\Lambda$) determines the uniform hyperbolicity of $\\Lambda$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-20T13:15:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A25",
      "37B20",
      "37C50",
      "37D20",
      "37D30"
    ],
    "keywords": [
      "invariant measures",
      "generic diffeomorphism",
      "non-uniform hyperbolicity",
      "generic subset",
      "accumulation measures"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.3439S"
    }
  }
}