{
  "id": "2010.03218",
  "version": "v1",
  "published": "2020-10-07T06:53:59.000Z",
  "updated": "2020-10-07T06:53:59.000Z",
  "title": "Chaos on compact manifolds: Differentiable synchronizations beyond Takens",
  "authors": [
    "Lyudmila Grigoryeva",
    "Allen Hart",
    "Juan-Pablo Ortega"
  ],
  "comment": "4 pages letter and 9 pages technical appendix",
  "categories": [
    "math.DS"
  ],
  "abstract": "This Letter shows that a large class of fading memory state-space systems driven by discrete-time observations of dynamical systems defined on compact manifolds always yields continuously differentiable synchronizations. This general result provides a powerful tool for the representation, reconstruction, and forecasting of chaotic attractors. It also adds to the literature on differentiable generalized synchronizations, whose existence was so far guaranteed for a restricted family of systems and was detected using H\\\"older exponent-based criteria.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-07T06:53:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact manifolds",
      "fading memory state-space systems driven",
      "general result",
      "large class",
      "yields continuously differentiable synchronizations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}