Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 1135–1169

DIMENSION OF THE REPELLER FOR A PIECEWISE EXPANDING AFFINE MAP

Balázs Bárány, Michal Rams and Károly Simon

Budapest University of Technology and Economics, Department of Stochastics, MTA-BME
Stochastics Research Group, P.O. Box 91, 1521 Budapest, Hungary; balubsheep 'at' gmail.com

Polish Academy of Sciences, Institute of Mathematics
ul. Śniadeckich 8, 00-656 Warszawa, Poland; rams 'at' impan.pl

Budapest University of Technology and Economics, Department of Stochastics
Institute of Mathematics, 1521 Budapest, P.O. Box 91, Hungary; simonk 'at' math.bme.hu

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 [42] and can be considered as the continuation of the works [5, 6] by the authors. We also present some applications of our results for generalized Takagi functions and fractal interpolation functions.

2010 Mathematics Subject Classification: Primary 28A80; Secondary 28A78.

Key words: Self-affine measures, self-affine sets, Hausdorff dimension.

Reference to this article: B. Bárány, M. Rams and K. Simon: Dimension of the repeller for a piecewise expanding affine map. Ann. Acad. Sci. Fenn. Math. 45 (2020), 1135–1169.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4560