Dimension of the repeller for a piecewise expanding affine map

Balázs Bárány, Michał Rams, Károly Simon

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)1135-1169
Number of pages35
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Volume45
Issue number2
DOIs
Publication statusPublished - 2020

Keywords

  • Hausdorff dimension
  • Self-affine measures
  • Self-affine sets

ASJC Scopus subject areas

  • Mathematics(all)

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