On Lebesgue Measure of Integral Self-Affine Sets

Ievgen V. Bondarenko; Rostyslav V. Kravchenko

doi:10.1007/s00454-010-9306-8

On Lebesgue Measure of Integral Self-Affine Sets

Ievgen V. Bondarenko, Rostyslav V. Kravchenko

Mathematics

Research output: Contribution to journal › Article

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 language	English (US)
Pages (from-to)	389-393
Number of pages	5
Journal	Discrete and Computational Geometry
Volume	46
Issue number	2
DOIs	https://doi.org/10.1007/s00454-010-9306-8
State	Published - 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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Bondarenko, I. V., & Kravchenko, R. V. (2011). On Lebesgue Measure of Integral Self-Affine Sets. Discrete and Computational Geometry, 46(2), 389-393. https://doi.org/10.1007/s00454-010-9306-8

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