Asymptotic decomposition of slow integral manifolds
type: Item
instance of: scholarly article
title: Asymptotic decomposition of slow integral manifolds
zbMATH Open document ID: 0855.34063
DOI: 10.1007/BF02104713
published in: Siberian Mathematical Journal
publication date: 1997-02-16T00:00:00Z
review text: The authors consider a singularly perturbed system of differential equations \(\varepsilon \dot z = Z(z,t, \varepsilon)\) under the assumption that the limit system of equations \(Z(z,t,0) = 0\) \((\varepsilon = 0)\) admits an \(m\)-parametric family of solutions \(z = \psi (v,t)\), \(v \in \mathbb{R}^m\), \(t \in \mathbb{R}\), where \(\psi\) is a sufficiently smooth vector function. They investigate the question of existence of an integral manifold of slow motions (a ``slow integral manifold'') \(z = P(v,t, \varepsilon)\) on which the motion is gouverned by an equation \(\dot v = Q (v,t, \varepsilon)\). The authors present several methods for computing such manifolds in the form of asymptotic expansions in powers of the small parameter \(\varepsilon\), and they obtain some results on their stability.
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34C30
Mathematics Subject Classification ID: 34C45
Mathematics Subject Classification ID: 34D35
zbMATH DE Number: 917135
zbMATH Keywords: singularly perturbed system
zbMATH Keywords: integral manifold of slow motions
zbMATH Keywords: asymptotic expansions
zbMATH Keywords: small parameters
zbMATH Keywords: stability
author: L. I. Kononenko
author: V. A. Sobolev
MaRDI profile type: Publication
cites work: Q4040184
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full work available at URL: https://doi.org/10.1007/bf02104713
OpenAlex ID: W1971762865
description: scientific article; zbMATH DE number 917135