{
  "id": "2202.03456",
  "version": "v1",
  "published": "2022-02-07T19:01:13.000Z",
  "updated": "2022-02-07T19:01:13.000Z",
  "title": "Distal systems in topological dynamics and ergodic theory",
  "authors": [
    "Nikolai Edeko",
    "Henrik Kreidler"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We generalize a result of Lindenstrauss on the interplay between measurable and topological dynamics which shows that every separable ergodic measurably distal dynamical system has a minimal distal model. We show that such a model can, in fact, be chosen completely canonically. The construction is performed by going through the Furstenberg--Zimmer tower of a measurably distal system and showing that at each step, there is a simple and canonical distal minimal model. This hinges on a new characterization of isometric extensions in topological dynamics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-07T19:01:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A05",
      "37B05"
    ],
    "keywords": [
      "topological dynamics",
      "distal system",
      "ergodic theory",
      "canonical distal minimal model",
      "ergodic measurably distal dynamical system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}