Chaos among self-maps of the Cantor space
type: Item
instance of: scholarly article
title: Chaos among self-maps of the Cantor space
zbMATH Open document ID: 1223.37042
author: Udayan B. Darji
author: Emma D'Aniello
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-06-20T00:00:00Z
review text: The authors prove that generic self-maps of the Cantor space have zero topological entropy. They prove that a generic self-map of a Cantor space has no periodic points and hence is not Devaney chaotic nor Devaney chaotic on any subsystem. They also deduce a dense subset of the space of all self-maps of the Cantor space in which each element of it is Devaney chaotic on some subsystem and also its topological entropy is infinite.
reviewed by: M. R. Molaei
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 5909857
zbMATH Keywords: Devaney chaos
zbMATH Keywords: entropy
zbMATH Keywords: generic map
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.03.065
OpenAlex ID: W2058191172
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DOI: 10.1016/J.JMAA.2011.03.065
description: scientific article; zbMATH DE number 5909857