{
  "id": "1608.05636",
  "version": "v1",
  "published": "2016-08-19T15:21:52.000Z",
  "updated": "2016-08-19T15:21:52.000Z",
  "title": "An autocorrelation and discrete spectrum for dynamical systems on metric spaces",
  "authors": [
    "Daniel Lenz"
  ],
  "comment": "15 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study dynamical systems $(X,G,m)$ with a compact metric space $X$ and a locally compact, $\\sigma$-compact, abelian group $G$. We show that such a system has discrete spectrum if and only if a certain space average over the metric is a Bohr almost periodic function. In this way, this average over the metric plays for general dynamical systems a similar role as the autocorrelation measure plays in the study of aperiodic order for special dynamical systems based on point sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-19T15:21:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete spectrum",
      "compact metric space",
      "autocorrelation measure plays",
      "abelian group",
      "study dynamical systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}