{
  "id": "math/0106032",
  "version": "v2",
  "published": "2001-06-05T20:57:48.000Z",
  "updated": "2002-06-18T11:41:32.000Z",
  "title": "Analytic non-linearizable uniquely ergodic diffeomorphisms on the two-torus",
  "authors": [
    "Maria Saprykina"
  ],
  "comment": "New corrected version",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the behavior of diffeomorphisms, contained in the closure $\\bar {\\A_\\a}$ (in the inductive limit topology) of the set $\\A_\\a$ of real-analytic diffeomorphisms of the torus $\\Bbb T^2$, conjugated to the rotation $R_\\a:(x,y)\\mapsto (x + \\a, y)$ by an analytic measure-preserving transformation. We show that for a generic $\\a\\in [0,1]$, $\\bar {\\A_\\a}$ contains a dense set of uniquely ergodic diffeomorphisms. We also prove that $\\bar {\\A_\\a}$ contains a dense set of diffeomorphisms that are minimal and non-ergodic.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-06-18T11:41:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A25",
      "37J40",
      "37A05"
    ],
    "keywords": [
      "analytic non-linearizable uniquely ergodic diffeomorphisms",
      "dense set",
      "inductive limit topology",
      "real-analytic diffeomorphisms",
      "analytic measure-preserving transformation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......6032S"
    }
  }
}