Smoothness of invariant manifolds for nonautonomous equations
type: Item
instance of: scholarly article
title: Smoothness of invariant manifolds for nonautonomous equations
zbMATH Open document ID: 1098.34041
author: Luís Barreira
author: Claudia Valls
published in: Communications in Mathematical Physics
publication date: 2006-03-21T00:00:00Z
review text: The authors investigate the smoothness of invariant manifolds for nonlinear equations of the form \[ v'=A(t)v+f(t,v) \] with zero solution under the weakest assumption on the linear part \(v' =A(t)v\), namely the existence of a nonuniform exponential dichotomy, e.g., for stable manifolds it is enough to assume that there exist negative Lyapunov exponents. The paper builds on [J. Differ. Equations 221, No.~1, 58--90 (2006; Zbl 1098.34036)] by the authors and proves \(C^1\) smoothness of the invariant manifolds of the trivial solution (cf. also with the authors [Nonlinearity 18, No.~5, 2373--2390 (2005; Zbl 1089.34040)] for higher regularity).
reviewed by: S. Siegmund
Mathematics Subject Classification ID: 34D09
Mathematics Subject Classification ID: 34C30
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 37D10
zbMATH DE Number: 5013703
zbMATH Keywords: invariant manifold
zbMATH Keywords: smoothness
MaRDI profile type: Publication
full work available at URL: s00220-005-1380-z
OpenAlex ID: W2088827347
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DOI: 10.1007/S00220-005-1380-Z
description: scientific article; zbMATH DE number 5013703