{
  "id": "0705.1073",
  "version": "v1",
  "published": "2007-05-08T12:17:02.000Z",
  "updated": "2007-05-08T12:17:02.000Z",
  "title": "Geometric representation of interval exchange maps over algebraic number fields",
  "authors": [
    "G. Poggiaspalla",
    "J. H. Lowenstein",
    "F. Vivaldi"
  ],
  "comment": "34 pages, 8 postscript figures",
  "doi": "10.1088/0951-7715/21/1/009",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we call the drift vector. We exhibit some examples of renormalizable interval exchange maps with zero and non-zero drift vector, and carry out some investigations of their properties. In particular, we look for evidence of the finite decomposition property: each lattice is the union of finitely many orbits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-08T12:17:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E05",
      "11Z05",
      "37E20"
    ],
    "keywords": [
      "algebraic number fields",
      "geometric representation",
      "interval exchange transformations",
      "non-zero drift vector",
      "finite decomposition property"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Nonlinearity",
      "year": 2008,
      "month": "Jan",
      "volume": 21,
      "number": 1,
      "pages": 149
    },
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008Nonli..21..149P"
    }
  }
}