{
  "id": "1103.3458",
  "version": "v1",
  "published": "2011-03-17T16:48:51.000Z",
  "updated": "2011-03-17T16:48:51.000Z",
  "title": "Local attractor continuation of non-autonomously perturbed systems",
  "authors": [
    "Martin Kell"
  ],
  "comment": "15 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Using Conley theory we show that local attractors remain (past) attractors under small non-autonomous perturbations. In particular, the attractors of the perturbed systems will have positive invariant neighborhoods and converge upper semicontinuously to the original attractor. The result is split into a finite-dimensional part (locally compact) and an infinite-dimensional part (not necessarily locally compact). The finite-dimensional part will be applicable to bounded random noise, i.e. continuous time random dynamical systems on a locally compact metric space which are uniformly close the unperturbed deterministic system. The \"closeness\" will be defined via a (simpler version of) convergence coming from singular perturbations theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-17T16:48:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B55",
      "37B35",
      "37L15",
      "37H99"
    ],
    "keywords": [
      "local attractor continuation",
      "non-autonomously perturbed systems",
      "locally compact",
      "finite-dimensional part",
      "compact metric space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.3458K"
    }
  }
}