Axiomatic definition of the topological entropy on the interval
type: Item
instance of: scholarly article
title: Axiomatic definition of the topological entropy on the interval
zbMATH Open document ID: 1021.37010
author: Lluís Alsedà
author: Jaume Llibre
author: Ľubomír Snoha
author: Sergiĭ Kolyada
published in: Aequationes Mathematicae
publication date: 2003-07-03T00:00:00Z
full work available at URL: http://hdl.handle.net/2117/808
review text: Let \(C(I)\) be the space of all \(I \to I\) continuous functions, \(I\) real compact interval . Two groups of axioms on a mapping \(A:C(I) \to [0,\infty]\) characterizing topological entropy are given. A map \(A:C(I) \to [0,\infty]\) is said to characterize chaos if for any \(f \in C(I)\) \(A(f)>0\) is equivalent to positive topological entropy of \(f\). A third group of axioms given in the paper is sufficient for a map \(A:C(I) \to [0,\infty]\) to characterize chaos. Neccessity of individual axioms is discussed.
Mathematics Subject Classification ID: 37B40
Mathematics Subject Classification ID: 26A18
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 1945916
zbMATH Keywords: topological entropy
zbMATH Keywords: axiomatic definition
zbMATH Keywords: chaos
zbMATH Keywords: pouring water
zbMATH Keywords: lower semicontinuity
zbMATH Keywords: semiconjugacy
reviewed by: Katarina Janková
MaRDI profile type: Publication
OpenAlex ID: W1524730809
DOI: 10.1007/S000100300008
description: scientific article; zbMATH DE number 1945916