Limit sets in product of semi-dynamical systems
type: Item
instance of: scholarly article
title: Limit sets in product of semi-dynamical systems
zbMATH Open document ID: 0938.54038
DOI: 10.1155/S0161171299223873
author: R. P. Bhagat
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2000-06-18T00:00:00Z
full work available at URL: https://eudml.org/doc/48437
review text: The paper is in continuation to the paper \textit{S. S. Prasad} and \textit{A. Kumar} [ibid. 7, No. 1, 181-185 (1984; Zbl 0562.54061)] and deals with the study of stability properties of products of semi-dynamical systems. A typical result is the following (Theorem 3.7): Let \((x_{\alpha },\Pi _{\alpha }),\alpha \in I,\) be a family of Lagrange stable and distal s.d.s. (semi-dynamical systems) and \((X,\Pi)\) be the product of s.d.s. Let \(x\in X\) and \(x=\left\{ x_{\alpha }\right\} .\) A motion \(\Pi (x,t)\) is Poisson stable in \((X,\Pi)\) if and only if \(\Pi _{\alpha }(X_{\alpha },t)\) is Poisson stable in \((X_{\alpha },\Pi _{\alpha }) \) for each \(\alpha \in I.\)
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47J35
zbMATH DE Number: 1334839
zbMATH Keywords: semi-dynamical system
zbMATH Keywords: Lagrange stability
zbMATH Keywords: Poisson stability
zbMATH Keywords: distality
zbMATH Keywords: limit sets
zbMATH Keywords: Cauchy net
reviewed by: Vasile Berinde
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1334839