Dynamical systems of finite-dimensional metric spaces and zero-dimensional covers
type: Item
instance of: scholarly article
title: Dynamical systems of finite-dimensional metric spaces and zero-dimensional covers
zbMATH Open document ID: 1295.54036
author: Yuki Ikegami
author: Hisao Kato
author: Akihide Ueda
published in: Topology and its Applications
publication date: 2013-02-27T00:00:00Z
full work available at URL: TIA 160-3l.pdf
review text: It is said that a dynamical system \((Y,g)\) \textit{covers} \((X,f)\) via an onto map \(p:Y\longrightarrow X\) provided that \(p\circ g=f\circ p\). In this paper, the authors, improving and generalizing a theorem by \textit{J. Kulesza} [Ergodic Theory Dyn. Syst. 15, No. 5, 939--950 (1995; Zbl 0882.54034)] to nonseparable metric spaces, prove the following main result: every metric \(n\)-dimensional dynamical system with zero-dimensional set of periodic points can be covered by a metric zero-dimensional dynamical system via an at most \(2^n\)-to-one closed map. They are also concerned with periodic dynamical systems.
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 54F45
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 55M10
Mathematics Subject Classification ID: 54C45
zbMATH DE Number: 6139374
zbMATH Keywords: dynamical systems
zbMATH Keywords: dimension
zbMATH Keywords: periodic points
zbMATH Keywords: zero-dimensional covers
zbMATH Keywords: general position
reviewed by: Salvador Hernández
MaRDI profile type: Publication
OpenAlex ID: W2024722244
DOI: 10.1016/J.TOPOL.2013.01.010
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description: scientific article; zbMATH DE number 6139374