Generic quasi-convergence for strongly order preserving semiflows: a new approach
type: Item
instance of: scholarly article
title: Generic quasi-convergence for strongly order preserving semiflows: a new approach
zbMATH Open document ID: 1074.34042
author: Morris W. Hirsch
author: Hal L. Smith
published in: Journal of Dynamics and Differential Equations
publication date: 2005-03-15T00:00:00Z
full work available at URL: 91d8608p
review text: The authors consider strongly order-preserving semiflows \(\Phi\) on partially ordered metric spaces \(X\), with \(\Phi\) having compact orbit closures. Let \(E\) denote the set of equilibria of \(\Phi\). Under the condition (L) Either every omega limit set has an infimum in \(X\) and the set of points that are doubly accessible from below (with respect to the order) has dense interior, or every omega limit set has a supremum in \(X\) and the set of points that are doubly accessible from above has dense interior, the authors prove that the set \(Q\) of points with limit set in \(E\) and the set \(C\subseteq Q\) of points with single point limit set satisfy \[ X\setminus Q\subseteq\overline{\text{Int\,}C}, \] and \(\text{Int\,}Q\) is dense in \(X\). An application to delay differential equations is given.
reviewed by: Gerd Herzog
Mathematics Subject Classification ID: 34C12
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 37C65
Mathematics Subject Classification ID: 37B99
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 2145897
zbMATH Keywords: Monotone dynamics
zbMATH Keywords: quasiconvergence
MaRDI profile type: Publication
OpenAlex ID: W2041464331
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DOI: 10.1007/S10884-004-4286-0
description: scientific article; zbMATH DE number 2145897