A characterization of zero topological entropy for a class of triangular mappings.
type: Item
instance of: scholarly article
title: A characterization of zero topological entropy for a class of triangular mappings.
zbMATH Open document ID: 1047.54022
DOI: 10.1016/S0022-247X(03)00566-3
author: Juan L. G. Guirao
author: Jacek Chudziak
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-01-06T00:00:00Z
review text: The paper gives a characterization of triangular maps \(F(x,y)=(f(x),g(x,y))\) of the unit square with basis map \(f\) having a closed set of periodic points. Such maps necessarily have zero topological entropy. Similar characterization of zero entropy is well-known in the case of continuous maps of the unit interval [see \textit{A. N. Sharkovsky}, \textit{S. F. Kolyada}, \textit{A. G. Sivak} and \textit{V. V. Fedorenko}, Dynamics of one-dimensional maps Mathematics and its Applications. 407. Dordrecht (1997; Zbl 0881.58020)]. It is also known that in the general case for triangular maps the same is not possible even in a particular case of triangular maps non-decreasing on the fibres.
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37E99
Mathematics Subject Classification ID: 37B20
Mathematics Subject Classification ID: 37B40
Mathematics Subject Classification ID: 26A18
zbMATH DE Number: 2022074
zbMATH Keywords: triangular maps
zbMATH Keywords: topological entropy
zbMATH Keywords: periodic, recurrent and uniformly recurrent points
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2022074