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- W4302411518 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 and fractal interpolation functions." @default.
- W4302411518 created "2022-10-06" @default.
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- W4302411518 date "2018-03-10" @default.
- W4302411518 modified "2023-10-16" @default.
- W4302411518 title "Dimension of the repeller for a piecewise expanding affine map" @default.
- W4302411518 doi "https://doi.org/10.48550/arxiv.1803.03788" @default.
- W4302411518 hasPublicationYear "2018" @default.
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