On the structure of uniform attractors
type: Item
instance of: scholarly article
title: On the structure of uniform attractors
zbMATH Open document ID: 0823.58033
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-08-15T00:00:00Z
review text: This paper presents several results concerning shape properties and properties related to robustness of the uniform attractors of continuous dynamical systems. It is proved that, in certain circumstances, small perturbations of a flow \(\pi\) produce new uniform attractors whose global properties (in the sense of shape theory) are comparable to those of the uniform attractors of \(\pi\). It is also proved that if \(K\) is a minimal compactum then the shape of the closure of every positive semitrajectory in the region of attraction of \(K\) is determined by \(K\). This result does not hold if one considers homotopy type instead of shape. Finally, a classical theorem of Karol Borsuk is used to determine the structure of the set of connected components of uniform attractors.
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37C70
zbMATH DE Number: 785128
zbMATH Keywords: uniform attractor
zbMATH Keywords: shape
zbMATH Keywords: robustness
zbMATH Keywords: minimal set
zbMATH Keywords: region of attraction
zbMATH Keywords: connected components
author: José Sanjurjo
reviewed by: José Sanjurjo
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1186
OpenAlex ID: W2078517233
DOI: 10.1006/JMAA.1995.1186
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description: scientific article; zbMATH DE number 785128