{
  "id": "1706.01006",
  "version": "v1",
  "published": "2017-06-03T23:35:11.000Z",
  "updated": "2017-06-03T23:35:11.000Z",
  "title": "On the Spectral Equivalence of Koopman Operators through Delay Embedding",
  "authors": [
    "Yoshihiko Susuki",
    "Kyoichi Sako",
    "Takashi Hikihara"
  ],
  "comment": "6 pages",
  "categories": [
    "math.DS",
    "nlin.CD"
  ],
  "abstract": "We provide one theorem of spectral equivalence of Koopman operators of an original dynamical system and its reconstructed one through the delay-embedding technique. The theorem is proved for measure-preserving maps (e.g. dynamics on compact attractors) and provides a mathematical foundation of computing spectral properties of the Koopman operators by a combination of extended dynamic mode decomposition and delay-embedding.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-03T23:35:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "koopman operators",
      "spectral equivalence",
      "delay embedding",
      "extended dynamic mode decomposition",
      "compact attractors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}