Stability for dynamical systems with first integrals: A topological criterion
type: Item
instance of: scholarly article
title: Stability for dynamical systems with first integrals: A topological criterion
zbMATH Open document ID: 0763.34041
DOI: 10.1016/0167-6911(92)90077-6
author: D. Aeyels
author: Rodolphe Sepulchre
published in: Systems \& Control Letters
publication date: 1993-04-01T00:00:00Z
review text: Let \(\Phi\) denote a continuous flow on an open set of \(\mathbb{R}^ n\) containing the origin \({\mathcal O}\). Assume that \({\mathcal O}\) is an equilibrium point for the flow. Further, assume that \(\Phi\) possesses a set of \(k\) continuous first integrals, \(G(x)=(G_ 1(x),\dots,G_ k(x))\), and denote by \(\Phi^ h\) the restriction of \(\Phi\) to the level set \(G(x)=h\). The authors prove that if \({\mathcal O}\) is an asymptotically stable equilibrium of \(\Phi^ 0\) (with respect to perturbations restricted to \(\Phi^ 0\)) then it is a stable equilibrium of the flow \(\Phi\).
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34D10
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 148046
zbMATH Keywords: continuous flow
zbMATH Keywords: equilibrium point
zbMATH Keywords: first integrals
zbMATH Keywords: asymptotically stable equilibrium
zbMATH Keywords: perturbations
MaRDI profile type: Publication
full work available at URL: 0167-6911(92)90077-6
OpenAlex ID: W2007634112
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description: scientific article; zbMATH DE number 148046