Admissibility versus nonuniform exponential behavior for noninvertible cocycles
type: Item
instance of: scholarly article
title: Admissibility versus nonuniform exponential behavior for noninvertible cocycles
zbMATH Open document ID: 1268.34101
author: Luís Barreira
author: Claudia Valls
published in: Discrete and Continuous Dynamical Systems
publication date: 2013-04-24T00:00:00Z
review text: From the abstract: We study the relation between the notions of exponential dichotomy and admissibility for a nonautonomous dynamics with discrete time. More precisely, we consider \(\mathbb{Z}\)-cocycles defined by a sequence of linear operators in a Banach space, and we give criteria for the existence of an exponential dichotomy in terms of the admissibility of the pairs \((\ell^p,\ell^q)\) of spaces of sequences, with \(p\leq q\) and \((p,q)\neq(1,\infty)\). We extend the existing results in several directions. Namely, we consider the general case of nonuniform exponential dichotomies; we consider \(\mathbb{Z}\)-cocycles and not only \(\mathbb{N}\)-cocycles; and we consider exponential dichotomies that need not be invertible in the stable direction. We also exhibit a collection of admissible pairs of spaces of sequences for any nonuniform exponential dichotomy.
reviewed by: Nguyen Van Minh
Mathematics Subject Classification ID: 34D09
Mathematics Subject Classification ID: 37D25
zbMATH DE Number: 6157253
zbMATH Keywords: Admissibility
zbMATH Keywords: nonuniform exponential dichotomies
MaRDI profile type: Publication
full work available at URL: dcds.2013.33.1297
OpenAlex ID: W2315601537
DOI: 10.3934/DCDS.2013.33.1297
description: scientific article; zbMATH DE number 6157253