{
  "id": "2011.14278",
  "version": "v1",
  "published": "2020-11-29T04:35:17.000Z",
  "updated": "2020-11-29T04:35:17.000Z",
  "title": "Nonsingular transformations that are ergodic with isometric coefficients and not weakly doubly ergodic",
  "authors": [
    "James Leng",
    "Cesar E. Silva"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We study two properties of nonsingular and infinite measure-preserving ergodic systems: weak double ergodicity, and ergodicity with isometric coefficients. We show that there exist infinite measure-preserving transformations that are ergodic with isometric coefficients but are not weakly doubly ergodic. We also give type $\\text{III}_\\lambda$ examples of such systems, $0<\\lambda\\leq 1$. We prove that under certain hypotheses, systems that are weakly mixing are ergodic with isometric coefficients and along the way we give an example of a uniformly rigid topological dynamical system along the sequence $(n_i)$ that is not measure theoretically rigid along $(n_i)$ for any nonsingular ergodic finite measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-29T04:35:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A40",
      "37A05",
      "37A50",
      "37A05",
      "37A50",
      "37A50"
    ],
    "keywords": [
      "isometric coefficients",
      "weakly doubly ergodic",
      "nonsingular transformations",
      "rigid topological dynamical system",
      "nonsingular ergodic finite measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}