{
  "id": "2209.01253",
  "version": "v1",
  "published": "2022-09-02T19:52:47.000Z",
  "updated": "2022-09-02T19:52:47.000Z",
  "title": "On rigidity properties of time-changes of unipotent flows",
  "authors": [
    "Mauro Artigiani",
    "Livio Flaminio",
    "Davide Ravotti"
  ],
  "comment": "41 pages, 3 figures. Comments are welcome!",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study time-changes of unipotent flows on finite volume quotients of simple linear groups, generalizing previous work by Ratner on time-changes of horocycle flows. Any measurable isomorphism between time-changes of unipotent flows gives rise to a non-trivial joining supported on its graph. Under a spectral gap assumption on the groups, we show the following rigidity result: either the only limit point of this graph joining under the action of a one-parameter renormalizing subgroup is the trivial joining, or the isomorphism is \"affine\", namely it is obtained composing an algebraic isomorphism with a (non-constant) translation along the centralizer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-02T19:52:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A17",
      "37A20"
    ],
    "keywords": [
      "unipotent flows",
      "rigidity properties",
      "spectral gap assumption",
      "simple linear groups",
      "finite volume quotients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}