{
  "id": "2206.06778",
  "version": "v1",
  "published": "2022-06-14T12:15:50.000Z",
  "updated": "2022-06-14T12:15:50.000Z",
  "title": "Description of tempered exponential dichotomies by admissibility with no Lyapunov norms",
  "authors": [
    "Davor Dragičević",
    "Weinian Zhang",
    "Linfeng Zhou"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Tempered exponential dichotomy formulates the nonuniform hyperbolicity for random dynamical systems. It was described by admissibility of a pair of function classes defined with Lyapunov norms, For MET-systems (systems satisfying the assumptions of multiplicative ergodic theorem (abbreviated as MET)), it can be described by admissibility of a pair without a Lyapunov norm. However, it is not known how to choose a suitable Lyapunov norms before a tempered exponential dichotomy is given, and there are examples of random systems which are not MET-systems but have a tempered exponential dichotomy. In this paper we give a description of tempered exponential dichotomy for general random systems, which may not be MET-systems, purely by measurable admissibility of three pairs of function classes with no Lyapunov norms. Further, restricting to the MET-systems, we obtain a simpler description of only one pair with no Lyapunov norms. Finally, we use our results to prove the roughness of tempered exponential dichotomies for parametric random systems and give a H\\\"older continuous dependence of the associated projections on the parameter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-14T12:15:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "admissibility",
      "description",
      "function classes",
      "met-systems",
      "tempered exponential dichotomy formulates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}