{
  "id": "1007.0707",
  "version": "v1",
  "published": "2010-07-05T15:47:30.000Z",
  "updated": "2010-07-05T15:47:30.000Z",
  "title": "Diffraction of limit periodic point sets",
  "authors": [
    "Michael Baake",
    "Uwe Grimm"
  ],
  "comment": "10 pages, 2 figures; paper presented at ICQ11 (Sapporo)",
  "journal": "Philosophical Magazine 91 (2011) 2661-2670",
  "doi": "10.1080/14786435.2010.508447",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Limit periodic point sets are aperiodic structures with pure point diffraction supported on a countably, but not finitely generated Fourier module that is based on a lattice and certain integer multiples of it. Examples are cut and project sets with p-adic internal spaces. We illustrate this by explicit results for the diffraction measures of two examples with 2-adic internal spaces. The first and well-known example is the period doubling sequence in one dimension, which is based on the period doubling substitution rule. The second example is a weighted planar point set that is derived from the classic chair tiling in the plane. It can be described as a fixed point of a block substitution rule.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-05T15:47:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "78A45",
      "52C23",
      "37B10",
      "42B10"
    ],
    "keywords": [
      "limit periodic point sets",
      "pure point diffraction",
      "period doubling substitution rule",
      "weighted planar point set",
      "block substitution rule"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Philosophical Magazine",
      "year": 2011,
      "month": "Jul",
      "volume": 91,
      "number": "19-21",
      "pages": 2661
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011PMag...91.2661B"
    }
  }
}