Generalized exponential dichotomy and global linearization
type: Item
instance of: scholarly article
title: Generalized exponential dichotomy and global linearization
zbMATH Open document ID: 1098.34042
author: Liangping Jiang
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-03-29T00:00:00Z
review text: The nonautonomous version of the Hartman-Grobman theorem was first proved by Palmer and establishes a topological conjugacy between a nonlinear system \[ x' = A(t)x + f(t,x) \] and its linearization \[ x' = A(t)x, \] under the assumption of \(f\) being bounded with small Lipschitz constant and the linear system admitting an exponential dichotomy. The contribution of this paper is to extend Palmer's results to systems with a linearization which only admits a generalized exponential dichotomy \[ | U(t) P U^{-1}(s)| \leq K \exp\left(- \int_s^t a(\tau) d\tau\right) , \quad t \geq s, \] for the fundamental matrix \(U\) and projection \(P\), with a positive, bounded and continuous function \(a\), and similarly for \(t \leq s\).
reviewed by: S. Siegmund
Mathematics Subject Classification ID: 34D09
Mathematics Subject Classification ID: 34C41
zbMATH DE Number: 5016142
zbMATH Keywords: generalized exponential dichotomy
zbMATH Keywords: topological equivalence
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.05.042
OpenAlex ID: W2016314509
cites work: A generalization of Hartman's linearization theorem
cites work: On Hartman's linearization theorem and Palmer's linearization theorem
DOI: 10.1016/J.JMAA.2005.05.042
description: scientific article; zbMATH DE number 5016142