Normally elliptic singular perturbations and persistence of homoclinic orbits
type: Item
instance of: scholarly article
title: Normally elliptic singular perturbations and persistence of homoclinic orbits
zbMATH Open document ID: 1227.34056
author: Nan Lu
author: Chongchun Zeng
published in: Journal of Differential Equations
publication date: 2011-04-08T00:00:00Z
full work available at URL: https://arxiv.org/abs/1012.0079
review text: This paper deals with a dynamical system, possibly infinite dimensional or non-autonomous, with fast and slow time scales which is oscillatory with high frequencies in the fast directions. Firstly, the limit system of the slow variables is derived and justified. Further, there are constructed the stable, the unstable, the center-stable, the center-unstable and the center manifold of the steady state of a size of order \(O(1)\), and their leading order approximations are given. Finally, using these tools, persistence of homoclinic solutions in this type of normally eliptic singular perturbation problem is investigated. In an appendix, a process to block-diagonalize the linearized system of the singularly perturbed system under consideration at a steady state is outlined.
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34E13
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34C45
zbMATH DE Number: 5876822
zbMATH Keywords: normally eliptic singular perturbation problems
zbMATH Keywords: homoclinic solutions
zbMATH Keywords: center manifolds
zbMATH Keywords: stable manifolds
zbMATH Keywords: unstable manifolds
zbMATH Keywords: high frequency oscillations
reviewed by: Vasile Dragan
MaRDI profile type: Publication
OpenAlex ID: W2963745976
arXiv ID: 1012.0079
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DOI: 10.1016/J.JDE.2011.02.001
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description: scientific article