Perturbed iterated function systems and the exact Hausdorff measure of their attractors
type: Item
instance of: scholarly article
title: Perturbed iterated function systems and the exact Hausdorff measure of their attractors
zbMATH Open document ID: 1203.28002
author: Nicholas Freeman
published in: Real Analysis Exchange
publication date: 2010-09-02T00:00:00Z
review text: The author defines a perturbed iterated function system (pIFS) in \(\mathbb R^d\). Then the attractor of such a system is introduced in a similar style to that of an IFS and such a set is proved to be unique. Then a partially perturbed iterated function system (ppIFS) was defined as a perturbed IFS with a constant tail. In a setup with similitudes and the strong separation condition, the author shows that a pIFS attractor can be approximated by a sequence of ppIFS attractors in such a way that the Hausdorff measure is preserved in the limit. Last the author uses this result to calculate the exact Hausdorff measure of the pIFS attractor from that of the limiting IFS.
Mathematics Subject Classification ID: 28A78
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 5778788
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: Hausdorff measure
zbMATH Keywords: perturbed iterated function system
zbMATH Keywords: attractor
MaRDI profile type: Publication
full work available at URL: realanalexch.35.1.0091
OpenAlex ID: W1568725201
DOI: 10.14321/REALANALEXCH.35.1.0091
description: scientific article; zbMATH DE number 5778788