{
  "id": "1010.3686",
  "version": "v1",
  "published": "2010-10-18T19:13:35.000Z",
  "updated": "2010-10-18T19:13:35.000Z",
  "title": "Periodic shadowing and $Ω$-stability",
  "authors": [
    "Alexey Osipov",
    "Sergei Yu. Pilyugin",
    "Sergey Tikhomirov"
  ],
  "comment": "21 pages",
  "journal": "Regul. Chaotic Dyn. 15 (2010), no. 2-3, 404-417",
  "doi": "10.1134/S1560354710020255",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that the following three properties of a diffeomorphism $f$ of a smooth closed manifold are equivalent: (i) $f$ belongs to the $C^1$-interior of the set of diffeomorphisms having periodic shadowing property; (ii) $f$ has Lipschitz periodic shadowing property; (iii) $f$ is $\\Omega$-stable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-18T19:13:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C50",
      "37D20"
    ],
    "keywords": [
      "lipschitz periodic shadowing property",
      "smooth closed manifold",
      "diffeomorphism",
      "equivalent"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Regular and Chaotic Dynamics",
      "year": 2010,
      "month": "Apr",
      "volume": 15,
      "number": "2-3",
      "pages": 404
    },
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010RCD....15..404O"
    }
  }
}