{
  "id": "1105.1277",
  "version": "v1",
  "published": "2011-05-06T13:02:24.000Z",
  "updated": "2011-05-06T13:02:24.000Z",
  "title": "Computer Assisted Proof for Normally Hyperbolic Invariant Manifolds",
  "authors": [
    "Maciej J. Capinski",
    "Carles Simo"
  ],
  "comment": "33 pages, 16 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We present a topological proof of the existence of a normally hyperbolic invariant manifold for maps. In our approach we do not require that the map is a perturbation of some other map for which we already have an invariant manifold. But a non-rigorous, good enough, guess is necessary. The required assumptions are formulated in a way which allows for rigorous computer assisted verification. We apply our method for a driven logistic map, for which non-rigorous numerical simulation in plain double precision suggests the existence of a chaotic attractor. We prove that this numerical evidence is false and that the attractor is a normally hyperbolic invariant curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-06T13:02:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "normally hyperbolic invariant manifold",
      "computer assisted proof",
      "normally hyperbolic invariant curve",
      "driven logistic map",
      "rigorous computer assisted verification"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/25/7/1997",
      "journal": "Nonlinearity",
      "year": 2012,
      "month": "Jul",
      "volume": 25,
      "number": 7,
      "pages": 1997
    },
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012Nonli..25.1997C"
    }
  }
}