On maps with dense orbits and the definition of chaos
type: Item
instance of: scholarly article
title: On maps with dense orbits and the definition of chaos
zbMATH Open document ID: 0758.58024
author: Stephen Silverman
published in: Rocky Mountain Journal of Mathematics
publication date: 1992-09-27T00:00:00Z
review text: The article deals with a chaotic behaviour in dynamical systems. The object is to examine the relationship between the axioms for the most popular definitions of chaos in discrete systems. The focus is on a definitive analysis in the case of one-dimensional manifold. The dynamical systems are considered on the interval, on the Cantor set, on the circle. It must be noticed the paper ``On the definition of chaos'' [Z. Angew. Math. Mech. 69, 175-185 (1989; Zbl 0713.58035)] by \textit{U. Kirchgraber} and \textit{D. Stoffer}, where the same problem is discussed in some other sense.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 34D30
zbMATH DE Number: 61938
zbMATH Keywords: dense orbit
zbMATH Keywords: periodic points
zbMATH Keywords: topologically transitive
zbMATH Keywords: chaotic behaviour
zbMATH Keywords: dynamical systems
zbMATH Keywords: discrete systems
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072815
OpenAlex ID: W2034426849
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DOI: 10.1216/RMJM/1181072815
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description: scientific article; zbMATH DE number 61938