{
  "id": "1301.2356",
  "version": "v1",
  "published": "2013-01-10T23:39:07.000Z",
  "updated": "2013-01-10T23:39:07.000Z",
  "title": "Hyperbolicity, transitivity and the two-sided limit shadowing property",
  "authors": [
    "Bernardo Carvalho"
  ],
  "comment": "10 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We explore the notion of two-sided limit shadowing property introduced by Pilyugin \\cite{P1}. Indeed, we characterize the $C^1$-interior of the set of diffeomorphisms with such a property on closed manifolds as the set of transitive Anosov diffeomorphisms. As a consequence we obtain that all codimention-one Anosov diffeomorphisms have the two-sided limit shadowing property. We also prove that every diffeomorphism $f$ with such a property on a closed manifold has neither sinks nor sources and is transitive Anosov (in the Axiom A case). In particular, no Morse-Smale diffeomorphism have the two-sided limit shadowing property. Finally, we prove that $C^1$-generic diffeomorphisms on closed manifolds with the two-sided limit shadowing property are transitive Anosov. All these results allow us to reduce the well-known conjecture about the transitivity of Anosov diffeomorphisms on closed manifolds to prove that the set of diffeomorphisms with the two-sided limit shadowing property coincides with the set of Anosov diffeomorphisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-10T23:39:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D20",
      "37C20"
    ],
    "keywords": [
      "closed manifold",
      "transitive anosov",
      "transitivity",
      "hyperbolicity",
      "codimention-one anosov diffeomorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.2356C"
    }
  }
}