A dynamical systems result on asymptotic integration of linear differential systems.
type: Item
instance of: scholarly article
title: A dynamical systems result on asymptotic integration of linear differential systems.
zbMATH Open document ID: 1037.34042
DOI: 10.1016/S0022-0396(02)00028-1
published in: Journal of Differential Equations
publication date: 2003-03-18T00:00:00Z
review text: The author studies, under a dynamical systems point of view, the asymptotic integration of linear differential systems of the form \(x^{\prime }=[\Lambda (t)+R(t)]x\), where \(\Lambda \) is diagonal and \(R\in L^{p}[t_{0},\infty )\) for \(p\in [ 1,2]\). By using the theory of linear skew-product flows, the paper presents a dichotomy condition in terms of the spectrum over the omega-limit set \(w_{\Lambda }\). The theory is illustrated by two examples that are not covered by the Hartman-Winter theorem.
Mathematics Subject Classification ID: 34D09
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34L05
zbMATH DE Number: 1884212
zbMATH Keywords: linear systems
zbMATH Keywords: asymptotic integration
zbMATH Keywords: spectral theory
author: Sigrun Bodine
reviewed by: Nicholas Karampetakis
MaRDI profile type: Publication
cites work: Asymptotic integration of linear differential equations
cites work: Asymptotic Representation of Solutions of Perturbed Systems of Linear Difference Equations
cites work: A new approach to asymptotic diagonalization of linear differential systems
cites work: Almost reducible systems
cites work: On the reduction of a system of linear equations to diagonal form
cites work: Dichotomies and reducibility
cites work: Dichotomies in stability theory
cites work: Q3992443
cites work: Harmonic analysis of the de Rham complex on the sphere.
cites work: Almost diagonal systems in asymptotic integration
cites work: Globally analytic simplification and the Levinson theorem
cites work: On the asymptotic integration of linear differential systems
cites work: A unified theory of asymptotic integration
cites work: Asymptotic Integrations of Linear Differential Equations
cites work: Q4224488
cites work: Analyticity of spectral subbundles
cites work: Smoothness of spectral subbundles and reducibility of quasi periodic linear differential systems
cites work: The asymptotic nature of solutions of linear systems of differential equations
cites work: Linear differential systems with conditionally integrable coefficients
cites work: Q5624175
cites work: Exponential dichotomy, integral separation and diagonalizability of linear systems of ordinary differential equations
cites work: Exponential dichotomies and transversal homoclinic points
cites work: Existence of dichotomies and invariant splittings for linear differential systems. I
cites work: Existence of dichotomies and invariant splittings for linear differential systems. II
cites work: A spectral theory for linear differential systems
cites work: Q5551835
cites work: Q5613838
description: scientific article; zbMATH DE number 1884212