{
  "id": "1609.09439",
  "version": "v1",
  "published": "2016-09-29T17:50:54.000Z",
  "updated": "2016-09-29T17:50:54.000Z",
  "title": "A note on shadowing properties",
  "authors": [
    "Hahng-Yun Chu",
    "Dae Hwan Goo",
    "Se-Hyun Ku"
  ],
  "comment": "9 pages. arXiv admin note: text overlap with arXiv:1305.2977 by other authors",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $\\mathfrak{X}^{1}(M)$ be the space of $C^{1}$-vector fields on $M$ endowed with the $C^{1}$-topology and let $\\Lambda$ be an isolated set for a $X\\in\\mathfrak{X}^{1}(M)$. In this paper, we directly prove that every $X\\in\\mathfrak{X}^{1}(M)$ having the (asymptotic) average shadowing property in $\\Lambda$ has no proper attractor in $\\Lambda$. Our proof is a direct version of the results by Gu and Ribeiro. We also show that every $X\\in\\mathfrak{X}^{1}(M)$ having the (two-sided) limit shadowing property with a gap in $\\Lambda$ is topologically transitive and has the shadowing property in $\\Lambda$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-29T17:50:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C50",
      "37C10",
      "54H20"
    ],
    "keywords": [
      "proper attractor",
      "vector fields",
      "limit shadowing property",
      "direct version",
      "average shadowing property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}