On the reduction to a subspace of stability properties of systems in metric spaces
type: Item
instance of: scholarly article
title: On the reduction to a subspace of stability properties of systems in metric spaces
zbMATH Open document ID: 0853.54038
DOI: 10.1007/BF01759358
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1996-05-14T00:00:00Z
review text: The authors deal with dynamical and semi-dynamical systems on metric spaces. Assume that two invariant subsets \(M\), \(Y\) are given, with \(M\) compact and \(M\subset Y\). The reduction problem consists in the following. If \(M\) is stable (or asymptotically stable) for the restriction of the dynamical system to \(Y\), under what additional assumptions is it possible to deduce that \(M\) is stable (or asymptotically stable) for the whole system? The authors prove several theorems about this problem, and compare their results to early achievements in the existing literature. In particular, the role of uniformity in the behaviour of the dynamical system is emphasized. As examples, systems in triangular form and systems with delays are discussed.
reviewed by: Andrea Bacciotti
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 34D30
zbMATH DE Number: 878434
author: Peter Seibert
author: José S. Florio
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01759358
OpenAlex ID: W1998249573
description: scientific article; zbMATH DE number 878434