{
  "id": "1710.00313",
  "version": "v1",
  "published": "2017-10-01T08:32:20.000Z",
  "updated": "2017-10-01T08:32:20.000Z",
  "title": "On the shadowing and limit shadowing properties",
  "authors": [
    "Noriaki Kawaguchi"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we deal with the relation between the shadowing property and the limit shadowing property. We prove that for any continuous self-map $f$ of a compact metric space, if $f$ has the limit shadowing property, then the restriction of $f$ to the non-wandering set satisfies the shadowing property. As an application, we prove the equivalence of the two shadowing properties for equicontinuous maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-01T08:32:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C50",
      "54H20",
      "37B20"
    ],
    "keywords": [
      "limit shadowing property",
      "compact metric space",
      "non-wandering set satisfies",
      "restriction",
      "continuous self-map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}