Topologically transitive homeomorphisms of quotients of tori
type: Item
instance of: scholarly article
title: Topologically transitive homeomorphisms of quotients of tori
zbMATH Open document ID: 0952.54024
author: Grant Cairns
author: Barry Jessup
author: Marcel Nicolau
published in: Discrete and Continuous Dynamical Systems
publication date: 2000-08-16T00:00:00Z
review text: This paper considers the following question: For what finite subgroups \(G \subseteq \text{GL} (n,\mathbb{Z})\), does an element \(A\in \text{GL} (n,\mathbb{Z})\) exist inducing a topologically transitive homeomorphism of \(T^n/ G\)? It is shown for \(n=2\) and 3, the only possibility is \(G= \{\pm I\}\). In higher dimension the structure is less restrictive, the authors give a variety of examples in dimension 4.
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 57S25
zbMATH DE Number: 1492570
reviewed by: T. S. Wu
MaRDI profile type: Publication
full work available at URL: dcds.1999.5.291
OpenAlex ID: W2066449583
DOI: 10.3934/DCDS.1999.5.291
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description: scientific article; zbMATH DE number 1492570