The optimal gap condition for invariant manifolds
type: Item
instance of: scholarly article
title: The optimal gap condition for invariant manifolds
zbMATH Open document ID: 0971.34044
author: N. Delaunay
published in: Discrete and Continuous Dynamical Systems
publication date: 2000-08-16T00:00:00Z
review text: The authors give optimal gap conditions using Lipschitz constants of the nonlinear terms and exponential estimates for the semiflows generated by the linear terms that imply the existence of infinite dimensional Lipschitz invariant manifolds for systems of weakly nonlinear equations on Banach spaces. The results are shown to imply the existence of invariant manifolds for skew-product flows generated by weakly nonlinear nonautonomous equations. Also, generalizations of results for the smoothness of invariant manifolds are given.
reviewed by: Norbert Koksch
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34C30
Mathematics Subject Classification ID: 35B42
Mathematics Subject Classification ID: 37L05
Mathematics Subject Classification ID: 37L15
Mathematics Subject Classification ID: 34K19
Mathematics Subject Classification ID: 37L25
Mathematics Subject Classification ID: 37C10
zbMATH DE Number: 1492569
zbMATH Keywords: invariant manifolds
zbMATH Keywords: gap condition
zbMATH Keywords: semilinear equations
zbMATH Keywords: nonautonomous equations
zbMATH Keywords: skew-product flows
MaRDI profile type: Publication
full work available at URL: dcds.1999.5.233
OpenAlex ID: W1991928371
DOI: 10.3934/DCDS.1999.5.233
description: scientific article; zbMATH DE number 1492569