Smooth robustness of parameterized perturbations of exponential dichotomies
type: Item
instance of: scholarly article
title: Smooth robustness of parameterized perturbations of exponential dichotomies
zbMATH Open document ID: 1204.39002
author: Luís Barreira
author: Claudia Valls
published in: Journal of Differential Equations
publication date: 2010-10-19T00:00:00Z
review text: Consider the nonautonomous linear difference equations \[ v_{m+1}=A_{m}v_{m}+B_{m}(\lambda )v_{m}\tag{\(*\)} \] in a Banach space, where \(\lambda \) is a parameter in some open subset of a Banach space, and where \(\lambda \mapsto B_{m}(\lambda )\) is of class \(C^1\) for each \(m\in\mathbb{Z}\). Assuming that the unperturbed dynamics \(v_{m+1}=A_mv_m\) has a nonuniform exponential dichotomy, the authors show that if the maps \(B_{m}\) are of class \(C^1\) in \(\lambda\), then the stable and unstable subspaces of the exponential dichotomies obtained from the perturbation are also of class \(C^1\) in \(\lambda \).
Mathematics Subject Classification ID: 39A06
zbMATH DE Number: 5802598
zbMATH Keywords: growth rates
zbMATH Keywords: robustness
zbMATH Keywords: linear difference equations
zbMATH Keywords: Banach space
zbMATH Keywords: exponential dichotomy
reviewed by: Fozi Dannan
MaRDI profile type: Publication
full work available at URL: j.jde.2010.06.011
OpenAlex ID: W2048710535
cites work: Q5431024
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DOI: 10.1016/J.JDE.2010.06.011
description: scientific article; zbMATH DE number 5802598