{
  "id": "1010.4937",
  "version": "v2",
  "published": "2010-10-24T07:22:36.000Z",
  "updated": "2011-03-04T13:32:32.000Z",
  "title": "Diffeomorphisms with various $C^1$ stable properties",
  "authors": [
    "Wenxiang Sun",
    "Xueting Tian"
  ],
  "comment": "8 pages",
  "journal": "Acta Mathematica Scientia 2012,32B(2):552-558",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $M$ be a smooth compact manifold and $\\Lambda$ be a compact invariant set. In this paper we prove that for every robustly transitive set $\\Lambda$, $f|_\\Lambda$ satisfies a $C^1-$generic-stable shadowable property (resp., $C^1-$generic-stable transitive specification property or $C^1-$generic-stable barycenter property) if and only if $\\Lambda$ is a hyperbolic basic set. In particular, $f|_\\Lambda$ satisfies a $C^1-$stable shadowable property (resp., $C^1-$stable transitive specification property or $C^1-$stable barycenter property) if and only if $\\Lambda$ is a hyperbolic basic set. Similar results are valid for volume-preserving case.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-03-04T13:32:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stable properties",
      "hyperbolic basic set",
      "transitive specification property",
      "diffeomorphisms",
      "shadowable property"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.4937S"
    }
  }
}