{
  "id": "1904.08285",
  "version": "v1",
  "published": "2019-04-17T14:20:21.000Z",
  "updated": "2019-04-17T14:20:21.000Z",
  "title": "Diffraction of a model set with complex windows",
  "authors": [
    "Michael Baake",
    "Uwe Grimm"
  ],
  "comment": "6 pages, 3 colour figures",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The well-known plastic number substitution gives rise to a ternary inflation tiling of the real line whose inflation factor is the smallest Pisot-Vijayaraghavan number. The corresponding dynamical system has pure point spectrum, and the associated control point sets can be described as regular model sets whose windows in two-dimensional internal space are Rauzy fractals with a complicated structure. Here, we calculate the resulting pure point diffraction measure via a Fourier matrix cocycle, which admits a closed formula for the Fourier transform of the Rauzy fractals, via a rapidly converging infinite product.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-17T14:20:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "11K70",
      "52C23"
    ],
    "keywords": [
      "model set",
      "complex windows",
      "well-known plastic number substitution",
      "resulting pure point diffraction measure",
      "rauzy fractals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}