On the structure of the attractors of hyperbolic iterated function systems
type: Item
instance of: scholarly article
title: On the structure of the attractors of hyperbolic iterated function systems
zbMATH Open document ID: 0941.37002
DOI: 10.1007/BF02677421
author: Qinghe Yin
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 1999-08-30T00:00:00Z
review text: The author presents the construction of attractors and Markov attractors for hyperbolic iterated function systems. By an iterated function system the author means a compact metric space \(X\) together with a collection of continuous maps \(T_1,\dots,T_n\) on it. If all the \(T_i\)'s are contractions then these iterated function systems are called hyperbolic. The author proves that when the Markov transition matrix \(M\) is an irreducible 0-1 matrix, for a huge amount of elements \((j_1,j_2,\dots)\in\Sigma_{M^t}\) the Markov attractor \(A_M\) can be approached by the set \[ \{T_{j_k}\circ T_{j_{k-1}}\circ\cdots\circ T_{j_1}x,\quad K\geq m\},\quad \forall x\in X. \]
Mathematics Subject Classification ID: 37A30
Mathematics Subject Classification ID: 37D25
zbMATH DE Number: 1328393
zbMATH Keywords: irreducible matrix
zbMATH Keywords: Markov attractors
zbMATH Keywords: hyperbolic iterated function systems
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02677421
OpenAlex ID: W30415561
description: scientific article; zbMATH DE number 1328393