On Lebesgue Measure of Integral Self-Affine Sets

Ievgen V. Bondarenko, Rostyslav V. Kravchenko

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

Let A be an expanding integer n×n matrix and D be a finite subset of Zn. The self-affine set T=T(A,D) is the unique compact set satisfying the equality A(T)=∪dD(T+d). We present an effective algorithm to compute the Lebesgue measure of the self-affine set T, the measure of the intersection T∩(T+u) for u∈Zn, and the measure of the intersection of self-affine sets T(A,D1)∩T(A,D2) for different sets D1, D2⊂Zn.

Original languageEnglish (US)
Pages (from-to)389-393
Number of pages5
JournalDiscrete and Computational Geometry
Volume46
Issue number2
DOIs
StatePublished - Sep 1 2011

Keywords

  • Graph-directed system
  • Self-affine set
  • Self-similar action
  • Tile

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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