Domains of attraction of generic \(\omega\)-limit sets for strongly monotone semiflows
type: Item
instance of: scholarly article
title: Domains of attraction of generic \(\omega\)-limit sets for strongly monotone semiflows
zbMATH Open document ID: 0764.58019
DOI: 10.4171/ZAA/452
author: Peter Takáč
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1992-08-13T00:00:00Z
review text: The asymptotic behaviour and the domain of attraction of a generic \(\omega\)-limit set of a strongly increasing semiflow in a strongly ordered metrizable space \(X\) are investigated. The author shows that if \(X\) is an open and order-convex subset of a separable strongly ordered Banach space then the \(\omega\)-unstable points are contained in the union of at most countably many Lipschitz manifolds of codimension 1. Thus ``almost all'' points are \(\omega\)-stable.
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 70K20
zbMATH DE Number: 40535
zbMATH Keywords: lower and upper \(\omega\)-limit sets
zbMATH Keywords: cooperative ODE
zbMATH Keywords: generic \(\omega\)- limit set
zbMATH Keywords: strongly increasing semiflow
reviewed by: Marian Mrozek
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 40535