Noninvertible cocycles: robustness of exponential dichotomies
type: Item
instance of: scholarly article
title: Noninvertible cocycles: robustness of exponential dichotomies
zbMATH Open document ID: 1268.47021
author: Claudia Valls
author: Luís Barreira
published in: Discrete and Continuous Dynamical Systems
publication date: 2012-11-12T00:00:00Z
review text: In this paper, considering discrete linear evolution processes (or cocycles) \(\{\mathcal{A}(m,n): m\geqslant n\}\) given by \(\mathcal{A}(m,n)=A_{m-1}\dots A_n\) if \(m>n\) and \(\mathcal{A}(m,m)=\operatorname{Id}\), for all \(m\in \mathbb{Z}\), where \((A_n)_{n\in \mathbb{Z}}\) is a family of bounded linear operators in a Banach space \(X\) and \(\operatorname{Id}\) is the identity operator in \(X\), the authors prove the robustness of uniform and nonuniform exponential dichotomies under small linear perturbations \((A_n+B_n)_{n\in \mathbb{Z}}\), with \((B_n)_{n\in \mathbb{Z}}\) being also a family of small (in some sense) bounded linear operators in \(X\). The results contemplate the case of discrete linear evolution processes which are not necessarily invertible in the stable direction.
reviewed by: Matheus Cheque Bortolan
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 37A20
Mathematics Subject Classification ID: 34D09
Mathematics Subject Classification ID: 34D10
Mathematics Subject Classification ID: 35B20
zbMATH DE Number: 6104843
zbMATH Keywords: robustness
zbMATH Keywords: exponential dichotomies
zbMATH Keywords: nonuniform exponential dichotomies
zbMATH Keywords: noninvertible dynamics
MaRDI profile type: Publication
full work available at URL: dcds.2012.32.4111
OpenAlex ID: W2325968858
DOI: 10.3934/DCDS.2012.32.4111
description: scientific article; zbMATH DE number 6104843