{
  "id": "1404.3545",
  "version": "v2",
  "published": "2014-04-14T11:39:53.000Z",
  "updated": "2014-08-11T15:36:06.000Z",
  "title": "Oriented shadowing property and $Ω$-stability for vector fields",
  "authors": [
    "Shaobo Gan",
    "Ming Li",
    "Sergey B. Tikhomirov"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We call that a vector field has the oriented shadowing property if for any $\\varepsilon>0$ there is $d>0$ such that each $d$-pseudo orbit is $\\varepsilon$-oriented shadowed by some real orbit. In this paper, we show that the $C^1$-interior of the set of vector fields with the oriented shadowing property is contained in the set of vector fields with the $\\Omega$-stability.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-11T15:36:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C50"
    ],
    "keywords": [
      "oriented shadowing property",
      "vector field",
      "pseudo orbit",
      "real orbit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.3545G"
    }
  }
}