{
  "id": "2111.10807",
  "version": "v1",
  "published": "2021-11-21T12:24:41.000Z",
  "updated": "2021-11-21T12:24:41.000Z",
  "title": "A convergence criterion for the unstable manifolds of the MacKay approximate renormalisation",
  "authors": [
    "Seul Bee Lee",
    "Stefano Marmi",
    "Tanja I. Schindler"
  ],
  "journal": "Phys. D: Nonlinear Phenom. 435 (2022)",
  "doi": "10.1016/j.physd.2022.133300",
  "categories": [
    "math.DS"
  ],
  "abstract": "We give an explicit arithmetical condition which guarantees the existence of the unstable manifold of the MacKay approximate renormalisation scheme for the breakup of invariant tori in one and a half degrees of freedom Hamiltonian systems, correcting earlier results. Furthermore, when our condition is violated, we give an example of points on which the unstable manifold does not converge.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-11-21T12:24:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J40",
      "37F50",
      "70H08"
    ],
    "keywords": [
      "unstable manifold",
      "convergence criterion",
      "mackay approximate renormalisation scheme",
      "freedom hamiltonian systems",
      "half degrees"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}