{
  "id": "1803.06402",
  "version": "v1",
  "published": "2018-03-16T21:15:43.000Z",
  "updated": "2018-03-16T21:15:43.000Z",
  "title": "Shadowing for nonautonomous dynamics",
  "authors": [
    "Lucas Backes",
    "Davor Dragicevic"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that whenever a sequence of invertible and bounded operators $(A_m)_{m\\in \\mathbb{Z}}$ acting on a Banach space $X$ admits an exponential dichotomy and a sequence of differentiable maps $f_m \\colon X\\to X$, $m\\in \\mathbb{Z}$, has bounded and H\\\"{o}lder derivatives, the nonautonomous dynamics given by $x_{m+1}=A_mx_m+f_m(x_m)$, $m\\in \\mathbb{Z}$ has various shadowing properties. Hence, we extend recent results of Bernardes Jr. et al. in several directions. As a nontrivial application of our results, we give a new proof of the nonautonomous Grobman-Hartman theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-16T21:15:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonautonomous dynamics",
      "banach space",
      "exponential dichotomy",
      "bernardes jr",
      "nontrivial application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}