Generating iterated function systems of some planar self-similar sets
type: Item
instance of: scholarly article
title: Generating iterated function systems of some planar self-similar sets
zbMATH Open document ID: 1305.28024
author: Yuanyuan Yao
published in: Journal of Mathematical Analysis and Applications
publication date: 2014-08-26T00:00:00Z
review text: Let \(E\) be a one-dimensional fractal self-similar set generated by an IFS satisfying a strong separation condition. Let \(E\times E\) be its product set. The author showed that for all IFSs generating \(E\times E\) the associated orthogonal matrices have at most 8 possibilities. The author also studied the structure of all IFSs that generate the planar self-similar sets satisfying both the strong separation condition and the convex open set condition.
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 6334572
zbMATH Keywords: planar self-similar set
zbMATH Keywords: iterating function system
zbMATH Keywords: minimal presentation
MaRDI profile type: Publication
full work available at URL: j.jmaa.2014.07.051
OpenAlex ID: W2051831874
cites work: Exact Hausdorff measure and intervals of maximum density for Cantor sets
cites work: Q5287506
cites work: Self-similar structure on intersections of triadic Cantor sets
cites work: On the equivalence of homogeneous iterated function systems
cites work: Self-similar and self-affine sets: measure of the intersection of two copies
cites work: On the structures of generating iterated function systems of Cantor sets
cites work: Q4739993
cites work: Q3731958
cites work: Self-similar structure on intersection of homogeneous symmetric Cantor sets
cites work: Q4527719
cites work: Q3232347
cites work: Resonance between Cantor sets
cites work: The Minimal Polynomial of cos(2π/n)
cites work: Self-similar structure on intersection of cartesian product of Cantor triadic sets with their translations
cites work: Self-similar structure on the intersection of middle-(1 − 2β) Cantor sets with β ∊ (1/3, 1/2)
DOI: 10.1016/J.JMAA.2014.07.051
description: scientific article; zbMATH DE number 6334572