{
  "id": "math/0501142",
  "version": "v1",
  "published": "2005-01-10T18:24:14.000Z",
  "updated": "2005-01-10T18:24:14.000Z",
  "title": "Mixing actions of the rationals",
  "authors": [
    "Richard Miles",
    "Tom Ward"
  ],
  "journal": "Ergodic Theory and Dynamical Systems, 26, No. 6, 1905-1911 (2006)",
  "doi": "10.1017/S0143385706000356",
  "categories": [
    "math.DS",
    "math.AC"
  ],
  "abstract": "We study mixing properties of algebraic actions of $\\mathbb Q^d$, showing in particular that prime mixing $\\mathbb Q^d$ actions on connected groups are mixing of all orders, as is the case for $\\mathbb Z^d$-actions. This is shown using a uniform result on the solution of $S$-unit equations in characteristic zero fields due to Evertse, Schlickewei and Schmidt. In contrast, algebraic actions of the much larger group $\\mathbb Q^*$ are shown to behave quite differently, with finite order of mixing possible on connected groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-01-10T18:24:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22D40",
      "37A15"
    ],
    "keywords": [
      "mixing actions",
      "algebraic actions",
      "connected groups",
      "characteristic zero fields",
      "finite order"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......1142M"
    }
  }
}