On invariant manifolds in singularly perturbed systems
type: Item
instance of: scholarly article
title: On invariant manifolds in singularly perturbed systems
zbMATH Open document ID: 0946.37020
DOI: 10.1023/A:1021739205527
author: O. D. Anosova
published in: Journal of Dynamical and Control Systems
publication date: 2000-04-13T00:00:00Z
review text: The author deals with a slow-fast system \[ \dot x=f(x,y, \varepsilon), \quad \dot y=\varepsilon g(x,y, \varepsilon), \quad \dot\varepsilon=0 \] where \(x\in\mathbb{R}^\ell\), \(y\in\mathbb{R}^m\), \(\varepsilon\in \mathbb{R}\). Assuming that the fast system \(\dot x=f(x,y,0)\), \(\dot y=0\) has a compact smooth invariant manifold with boundary \(M_0=M_0(y)\) smoothly depending on \(y\), where \(y\) runs over some ball \(B\subset \mathbb{R}^m\), the author proves that for a sufficiently small \(\varepsilon\), the whole system has an invariant manifold close to \(\bigcup_{y\in B}M_0(g) \times\{y\}\). The degree of its smoothness is analyzed.
Mathematics Subject Classification ID: 37D10
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 37C10
zbMATH DE Number: 1431895
zbMATH Keywords: singularly perturbed system
zbMATH Keywords: slow-fast system
zbMATH Keywords: invariant manifold
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1431895