{
  "id": "1808.08787",
  "version": "v1",
  "published": "2018-08-27T11:31:16.000Z",
  "updated": "2018-08-27T11:31:16.000Z",
  "title": "The numerical computation of unstable manifolds for infinite dimensional dynamical systems by embedding techniques",
  "authors": [
    "Adrian Ziessler",
    "Michael Dellnitz",
    "Raphael Gerlach"
  ],
  "categories": [
    "math.DS",
    "math.NA"
  ],
  "abstract": "In this work we extend the novel framework developed by Dellnitz, Hessel-von Molo and Ziessler to the computation of finite dimensional unstable manifolds of infinite dimensional dynamical systems. To this end, we adapt a set-oriented continuation technique developed by Dellnitz and Hohmann for the computation of such objects of finite dimensional systems with the results obtained in the work of Dellnitz, Hessel-von Molo and Ziessler. We show how to implement this approach for the analysis of partial differential equations and illustrate its feasibility by computing unstable manifolds of the one-dimensional Kuramoto-Sivashinsky equation as well as for the Mackey-Glass delay differential equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-27T11:31:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B42",
      "37L25",
      "37M99"
    ],
    "keywords": [
      "infinite dimensional dynamical systems",
      "numerical computation",
      "embedding techniques",
      "mackey-glass delay differential equation",
      "hessel-von molo"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}