{
  "id": "1510.05843",
  "version": "v1",
  "published": "2015-10-20T11:49:30.000Z",
  "updated": "2015-10-20T11:49:30.000Z",
  "title": "Takens embedding theorem with a continuous observable",
  "authors": [
    "Yonatan Gutman"
  ],
  "comment": "To appear in Proceedings of the Erg. Th. Workshops UNC Chapel Hill 2013-2014",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Let $(X,T)$ be a dynamical system where $X$ is a compact metric space and $T:X\\rightarrow X$ is continuous and invertible. Assume the Lebesgue covering dimension of $X$ is $d$. We show that for a generic continuous map $h:X\\rightarrow[0,1]$, the $(2d+1)$-delay observation map $x\\mapsto\\big(h(x),h(Tx),\\ldots,h(T^{2d}x)\\big)$ is an embedding of $X$ inside $[0,1]^{2d+1}$. This is a generalization of the discrete version of the celebrated Takens embedding theorem, as proven by Sauer, Yorke and Casdagli to the setting of a continuous observable. In particular there is no assumption on the (lower) box-counting dimension of $X$ which may be infinite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-20T11:49:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C45",
      "54H20"
    ],
    "keywords": [
      "continuous observable",
      "compact metric space",
      "delay observation map",
      "generic continuous map",
      "celebrated takens embedding theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151005843G"
    }
  }
}