An existence theorem of smooth nonlocal center manifolds for systems close to a system with a homoclinic loop
type: Item
instance of: scholarly article
title: An existence theorem of smooth nonlocal center manifolds for systems close to a system with a homoclinic loop
zbMATH Open document ID: 0940.37010
author: M. V. Shashkov
author: D. Turaev
published in: Journal of Nonlinear Science
publication date: 2000-05-01T00:00:00Z
review text: Considered are systems of differential equations close to a system that has a homoclinic loop. The study of the dynamics of such systems is facilitated by a dimensional reduction achieved through the construction of a locally invariant center manifold that contains all limit sets. Such invariant center manifolds were constructed by a number of people: The theses of Turaev and Sandstede, the reviewer [Mem. Am. Math. Soc. 578 (1996; Zbl 0862.34042)] and the paper [J. Differ. Equ. 126, 1-47 (1996; Zbl 0849.34036)] by \textit{R. Rousseau} and \textit{C. Roussarie}. In this paper the authors give a detailed proof of the existence of invariant center manifolds for systems of differential equations that are merely continuously differentiable. Orbits are controled by considering them as solutions to boundary value problems, a successful approach in bifurcation theory developed in this context by Shil'nikov.
reviewed by: Ale Jan Homburg
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37C29
zbMATH DE Number: 1347341
zbMATH Keywords: locally invariant center manifold
MaRDI profile type: Publication
full work available at URL: s003329900078
OpenAlex ID: W2159145420
DOI: 10.1007/S003329900078
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description: scientific article; zbMATH DE number 1347341