On the dimension of self-affine sets and measures with overlaps

Balázs Bárány, Michałrams, K. Simon

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In this paper we consider diagonally affine, planar IFS Φ = {Si(x, y)=(αix +ti,1, βiy +ti,2)}m i=1. Combining the techniques of Hochman and Feng and Hu, we compute the Hausdorff dimension of the self-affine attractor and measures and we give an upper bound for the dimension of the exceptional set of parameters.

Original languageEnglish
Pages (from-to)4427-4440
Number of pages14
JournalProceedings of the American Mathematical Society
Volume144
Issue number10
DOIs
Publication statusPublished - Oct 1 2016

Fingerprint

Exceptional Sets
Self-affine
Hausdorff Dimension
Attractor
Overlap
Upper bound

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

On the dimension of self-affine sets and measures with overlaps. / Bárány, Balázs; Michałrams, ; Simon, K.

In: Proceedings of the American Mathematical Society, Vol. 144, No. 10, 01.10.2016, p. 4427-4440.

Research output: Contribution to journalArticle

Bárány, Balázs ; Michałrams, ; Simon, K. / On the dimension of self-affine sets and measures with overlaps. In: Proceedings of the American Mathematical Society. 2016 ; Vol. 144, No. 10. pp. 4427-4440.
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