Topological mapping properties defined by digraphs
type: Item
instance of: scholarly article
title: Topological mapping properties defined by digraphs
zbMATH Open document ID: 0957.54020
author: John Banks
published in: Discrete and Continuous Dynamical Systems
publication date: 2000-08-16T00:00:00Z
review text: Let \(f:X\to X\) be a continuous map on the topological space \(X\) given by the family \({\mathcal S}\) of open sets. A graph \(G\) with directed edges \((u,v)\) \((u,v\in G)\) defines a mapping property if for any \(\varphi:G\to S\smallsetminus \emptyset\) there is \(k\geq 1\) such that \(f^k (\varphi(u))\cap \varphi(v)\neq \emptyset\) for every edge \((u,v)\) in \(G\). Several graphs are listed in the paper under review (including the non-wandering, transitivity and mixing properties) and their classification is given.
reviewed by: Manfred Denker
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37B20
Mathematics Subject Classification ID: 28D99
zbMATH DE Number: 1492566
zbMATH Keywords: topological weak mixing
zbMATH Keywords: mapping property
zbMATH Keywords: non-wandering
zbMATH Keywords: transitivity
MaRDI profile type: Publication
full work available at URL: dcds.1999.5.83
OpenAlex ID: W2041236345
DOI: 10.3934/DCDS.1999.5.83
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description: scientific article; zbMATH DE number 1492566