A new approach to asymptotic diagonalization of linear differential systems
type: Item
instance of: scholarly article
title: A new approach to asymptotic diagonalization of linear differential systems
zbMATH Open document ID: 0957.34010
DOI: 10.1023/A:1009054904419
author: Robert J. Sacker
author: Sigrun Bodine
published in: Journal of Dynamics and Differential Equations
publication date: 2001-03-19T00:00:00Z
review text: The authors study the asymptotic diagonalization of systems \[ \dot{x} = [\Lambda(t) + P(t) + R(t)]x \quad \text{in } \mathbb{R}^n \] where \(\Lambda\) is an \(L_{\text{loc}}^p\)-matrix, \(P\) is \(L^m\) and \(R\) is \(L^1\), \(p,m \in [1,\infty)\). Using linear skew-product flows and spectral theory, the authors show that if the unperturbed system \[ \dot{x} = \Lambda(t) x \] has full spectrum (i.e. \(n\) spectral intervals) over its hull, then the entire system is asymptotically diagonalizable almost everywhere.
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34L05
zbMATH DE Number: 1453232
zbMATH Keywords: linear systems
zbMATH Keywords: asymptotic diagonalization
zbMATH Keywords: spectral theory
reviewed by: S. Siegmund
MaRDI profile type: Publication
full work available at URL: a:1009054904419
OpenAlex ID: W1532062645
description: scientific article; zbMATH DE number 1453232