{
  "id": "1409.2645",
  "version": "v1",
  "published": "2014-09-09T09:07:51.000Z",
  "updated": "2014-09-09T09:07:51.000Z",
  "title": "Distribution of Patches in Tilings and Spectral Properties of Corresponding Dynamical Systems",
  "authors": [
    "Yasushi Nagai"
  ],
  "comment": "24pages, 4 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "A tiling is a cover of R^d by tiles such as polygons that overlap only on their borders. A patch is a configuration consisting of finitely many tiles that appears in tilings. From a tiling, we can construct a dynamical system which encodes the nature of the tiling. In the literature, properties of this dynamical system were investigated by studying how patches distribute in each tiling. In this article we conversely research distribution of patches from properties of the corresponding dynamical systems. We show periodic structures are hidden in tilings which are not necessarily periodic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-09T09:07:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "corresponding dynamical systems",
      "spectral properties",
      "periodic structures",
      "patches distribute",
      "conversely research distribution"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/28/8/2617",
      "journal": "Nonlinearity",
      "year": 2015,
      "month": "Aug",
      "volume": 28,
      "number": 8,
      "pages": 2617
    },
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015Nonli..28.2617N"
    }
  }
}