{
  "id": "2308.01467",
  "version": "v1",
  "published": "2023-08-02T23:07:32.000Z",
  "updated": "2023-08-02T23:07:32.000Z",
  "title": "EDMD for expanding circle maps and their complex perturbations",
  "authors": [
    "Oscar F. Bandtlow",
    "Wolfram Just",
    "Julia Slipantschuk"
  ],
  "comment": "18 pages, 4 figures",
  "categories": [
    "math.DS",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "We show that spectral data of the Koopman operator arising from an analytic expanding circle map $\\tau$ can be effectively calculated using an EDMD-type algorithm combining a collocation method of order m with a Galerkin method of order n. The main result is that if $m \\geq \\delta n$, where $\\delta$ is an explicitly given positive number quantifying by how much $\\tau$ expands concentric annuli containing the unit circle, then the method converges and approximates the spectrum of the Koopman operator, taken to be acting on a space of analytic hyperfunctions, exponentially fast in n. Additionally, these results extend to more general expansive maps on suitable annuli containing the unit circle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-02T23:07:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C30",
      "37E10",
      "30H10"
    ],
    "keywords": [
      "complex perturbations",
      "koopman operator",
      "unit circle",
      "expands concentric annuli",
      "analytic expanding circle map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}