{
  "id": "2002.01310",
  "version": "v1",
  "published": "2020-02-01T12:55:59.000Z",
  "updated": "2020-02-01T12:55:59.000Z",
  "title": "Quasi-shadowing for partially hyperbolic dynamics on Banach spaces",
  "authors": [
    "Lucas Backes",
    "Davor Dragicevic"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1905.08251",
  "categories": [
    "math.DS"
  ],
  "abstract": "A partially hyperbolic dynamical system is said to have the quasi-shadowing property if every pseudotrajectory can be shadowed by a sequence of points $(x_n)_{n\\in \\Z}$ such that $x_{n+1}$ is obtained from the image of $x_n$ by moving it by a small factor in the central direction. In the present paper, we prove that a small nonlinear perturbation of a partially dichotomic sequence of (not necessarily invertible) linear operators acting on an arbitrary Banach space has the quasi-shadowing property. We also get obtain a continuous time version of this result. As an application of our main result, we prove that a certain class of partially dichotomic sequences of linear operators is stable up to the movement in the central direction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-01T12:55:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "partially hyperbolic dynamics",
      "partially dichotomic sequence",
      "central direction",
      "linear operators",
      "arbitrary banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}