{
  "id": "1812.05483",
  "version": "v1",
  "published": "2018-12-13T15:34:36.000Z",
  "updated": "2018-12-13T15:34:36.000Z",
  "title": "Rigidity of joinings for some measure preserving systems",
  "authors": [
    "Changguang Dong",
    "Adam Kanigowski",
    "Daren Wei"
  ],
  "comment": "27 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We introduce two properties: strong R-property and $C(q)$-property, describing a special way of divergence of nearby trajectories for an abstract measure preserving system. We show that systems satisfying the strong R-property are disjoint (in the sense of Furstenberg) with systems satisfying the $C(q)$-property. Moreover, we show that if $u_t$ is a unipotent flow on $G/\\Gamma$ with $\\Gamma$ irreducible, then $u_t$ satisfies the $C(q)$-property provided that $u_t$ is not of the form $h_t\\times\\operatorname{id}$, where $h_t$ is the classical horocycle flow. Finally, we show that the strong R-property holds for all (smooth) time changes of horocycle flows and non-trivial time changes of bounded type Heisenberg nilflows.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-13T15:34:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "horocycle flow",
      "abstract measure preserving system",
      "strong r-property holds",
      "non-trivial time changes",
      "bounded type heisenberg nilflows"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}