{
  "id": "1803.03788",
  "version": "v1",
  "published": "2018-03-10T10:33:03.000Z",
  "updated": "2018-03-10T10:33:03.000Z",
  "title": "Dimension of the repeller for a piecewise expanding affine map",
  "authors": [
    "Balázs Bárány",
    "Michał Rams",
    "Károly Simon"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we study the dimension theory of a class of piecewise affine systems in euclidean spaces suggested by Michael Barnsley, with some applications to the fractal image compression. It is a more general version of the class considered in the work of Keane, Simon and Solomyak [The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition. {\\it Fund. Math.}, {\\bf 180}(3):279-292, 2003] and can be considered as the continuation of the works [On the dimension of self-affine sets and measures with overlaps. {\\it Proc. Amer. Math. Soc.}, {\\bf 144}(10):4427-4440, 2016], [On the dimension of triangular self-affine sets. {\\it Erg. Th. \\& Dynam. Sys.}, to appear.] by the authors. We also present some applications of our results for the generalized Takagi functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-10T10:33:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A78",
      "28A80"
    ],
    "keywords": [
      "piecewise expanding affine map",
      "fractal image recognition",
      "application",
      "triangular self-affine sets",
      "fractal image compression"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}