{
  "id": "1206.6717",
  "version": "v2",
  "published": "2012-06-28T15:02:05.000Z",
  "updated": "2012-11-24T01:16:59.000Z",
  "title": "Grobman-Hartman theorems for diffeomorphisms of Banach spaces over valued fields",
  "authors": [
    "Helge Glockner"
  ],
  "comment": "LaTeX; v2: 33 pages, discussion of parameter dependence of local conjugacies added, some minor corrections",
  "categories": [
    "math.DS"
  ],
  "abstract": "Consider a local diffeomorphism f of an ultrametric Banach space over an ultrametric field, around a hyperbolic fixed point x. We show that, locally, the system is topologically conjugate to the linearized system. An analogous result is obtained for local diffeomorphisms of real p-Banach spaces (like l^p) for 0 < p =< 1. More generally, we obtain a local linearization if f is merely a local homeomorphism which is strictly differentialble at a hyperbolic fixed point x. Also a new global version of the Grobman-Hartman theorem is provided. It applies to Lipschitz perturbations of hyperbolic automorphisms of Banach spaces over valued fields. The local conjugacies H constructed are not only homeomorphisms, but H and H^{-1} are Hoelder. We also study the dependence of H and H^{-1} on f (keeping x and f'(x) fixed).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-24T01:16:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C15",
      "26E30",
      "46A16",
      "46S10"
    ],
    "keywords": [
      "grobman-hartman theorem",
      "valued fields",
      "hyperbolic fixed point",
      "local diffeomorphism",
      "ultrametric banach space"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.6717G"
    }
  }
}