Discrete dynamical systems in \(L\)-topological spaces
type: Item
instance of: scholarly article
title: Discrete dynamical systems in \(L\)-topological spaces
zbMATH Open document ID: 1086.54005
author: Li Chen
author: Hui Kou
author: Maokang Luo
author: Weinian Zhang
published in: Fuzzy Sets and Systems
publication date: 2006-01-24T00:00:00Z
review text: The study is focused on an analysis of some properties of discrete dynamic systems defined in \(L\)-topological spaces. The description of such systems is based upon the definitions of \(L\)-image and \(L\)-preimage operators, \[ \begin{aligned} f^\rightarrow(A)(y) &=\vee\{A(t): t\in X, f(t)= y\}\,A\in L^X,\;y\in Y,\\ f^\leftarrow(B)(x) &= B(f(x))\,B\in L^Y,\;x\in X,\end{aligned} \] where \(L\) denotes a completely distributive lattice. The family \(\{f^{\rightarrow n},n\in\mathbb{Z}\}\) defines a discrete dynamical system in \((L^X,\delta)\) with \(\delta\) being the \(L\)-topology on \(X\). (\(f^{\rightarrow-n}= f^{\leftarrow n}\), \(n= 0,1,2,\dots\) assuming that \(f\) is a homeomorphism). Studied are the key issues of such dynamical systems, namely their topological mixing, transitivity, and minimality. In the sequel, these aspects are compared with their counterparts existing in nonfuzzy spaces.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 5001333
zbMATH Keywords: \(L\)-topology
zbMATH Keywords: Zadeh image operator
zbMATH Keywords: dynamical system
zbMATH Keywords: nonwandering point
zbMATH Keywords: topological mixing
reviewed by: Witold Pedrycz
MaRDI profile type: Publication
full work available at URL: j.fss.2005.05.026
OpenAlex ID: W1976276241
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DOI: 10.1016/J.FSS.2005.05.026
description: scientific article; zbMATH DE number 5001333