Dimension of the repeller for a piecewise expanding affine map

Bárány, Balázs and Rams, Michal and Simon, Károly (2020) Dimension of the repeller for a piecewise expanding affine map. Annales Academiae Scientiarum Fennicae Mathematica, 45 (2). pp. 1135-1169. ISSN 1798-2383

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Abstract

In this paper, we study the dimension theory of a class of piecewise affine systems in euclidean spaces suggested by 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 and can be considered as the continuation of the works by the authors. We also present some applications of our results for generalized Takagi functions and fractal interpolation functions.

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