Rigidity of infinite one-dimensional iterated function systems
type: Item
instance of: scholarly article
title: Rigidity of infinite one-dimensional iterated function systems
zbMATH Open document ID: 0945.28005
author: Pavel Hanus
author: Mariusz Urbański
published in: Real Analysis Exchange
publication date: 2000-05-21T00:00:00Z
review text: Let \(X \subset \mathbb R\) be a compact interval and \(I\) be a countable set containing at least two elements. Let \(S = \{\varphi _i:X \to X;\;i \in I\}\) be a collection of injective contractions of \(X\) into \(X\) such that there exists \(s \in (0,1)\) with \(|\varphi _i(x) - \varphi _i(y)|\leq s|x-y|\) for every \(i \in I,\;x,y \in X\). Then \(S\) is called an iterated function system. The authors study a special class of iterated function systems, so-called conformal iterated function systems, which were introduced in the paper by \textit{R. D. Mauldin} and \textit{M. Urbański} [Proc. Lond. Math. Soc., III. Ser. 73, No. 1, 105-154 (1996; Zbl 0852.28005)]. The sufficient and necessary conditions, under which two conformal systems of bounded geometry are bi-Lipschitz equivalent, are proved. The authors deals also with real analytic systems and scaling functions.
reviewed by: M. Zelený
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 37E05
Mathematics Subject Classification ID: 26A18
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 1449517
zbMATH Keywords: iterated function system
zbMATH Keywords: conformal systems
zbMATH Keywords: real-analytic systems
zbMATH Keywords: bi-Lipschitz equivalent systems
zbMATH Keywords: IFS
zbMATH Keywords: scaling functions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1449517