Exponential dichotomy for asymptotically hyperbolic two-dimensional linear systems
type: Item
instance of: scholarly article
title: Exponential dichotomy for asymptotically hyperbolic two-dimensional linear systems
zbMATH Open document ID: 1226.34048
author: Weishi Liu
author: E. Van Vleck
published in: Journal of Dynamics and Differential Equations
publication date: 2011-01-07T00:00:00Z
review text: This article focuses on the non-autonomous differential equation \[ y''- q(t)\,y = 0,\quad t\in \mathbb R, \] where \(q\) is assumed to be continuous and asymptotically constant. The central problem is the question whether the associated first order linear system admits exponential dichotomy. This question is studied via rigorous perturbation methods combined with numerical techniques.
Mathematics Subject Classification ID: 34D09
Mathematics Subject Classification ID: 34D10
zbMATH DE Number: 5833832
zbMATH Keywords: exponential dichotomy
zbMATH Keywords: Sacker-Sell spectrum
zbMATH Keywords: QR methods
MaRDI profile type: Publication
full work available at URL: s10884-010-9170-5
OpenAlex ID: W2036601166
cites work: Q4856188
cites work: Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. I: Theory
cites work: Stability of traveling waves: dichotomies and eigenvalue conditions on finite intervals
cites work: Resonance tongues in Hill's equations: A geometric approach
cites work: Q4258125
cites work: Existence and roughness of the exponential dichotomy for skew-product semiflow in Banach spaces
cites work: Center manifolds for smooth invariant manifolds
cites work: Floquet bundles for scalar parabolic equations
cites work: Q5848416
cites work: Homoclinic shadowing
cites work: Dichotomies in stability theory
cites work: Exponential dichotomy on the real line: SVD and QR methods
cites work: Computation of orthonormal factors for fundamental solution matrices
cites work: Lyapunov Spectral Intervals: Theory and Computation
cites work: On the error in computing Lyapunov exponents by QR methods
cites work: Perturbation theory for approximation of Lyapunov exponents by QR methods
cites work: Lyapunov and Sacker-Sell spectral intervals
cites work: On the Error in QR Integration
cites work: Q5798251
cites work: Q5658861
cites work: Q3871201
cites work: Q3933274
cites work: Geometric theory of semilinear parabolic equations
cites work: The Oseledec and Sacker-Sell Spectra for Almost Periodic Linear Systems: An Example
cites work: Ergodic Properties of Linear Dynamical Systems
cites work: Q3943431
cites work: Q5540675
cites work: Q5565849
cites work: Exponential Dichotomies and Fredholm Operators
cites work: Robustness of exponential dichotomies in infinite-dimensional dynamical systems
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: Existence of dichotomies and invariant splittings for linear differential systems. III
cites work: A spectral theory for linear differential systems
cites work: Dichotomies for linear evolutionary equations in Banach spaces
cites work: Dynamics of evolutionary equations
cites work: Q4550350
cites work: Absolute and convective instabilities of waves on unbounded and large bounded domains
cites work: Asymptotically autonomous differential equations in the plane
cites work: On the Error in the Product QR Decomposition
cites work: Determining Lyapunov exponents from a time series
DOI: 10.1007/S10884-010-9170-5
description: scientific article; zbMATH DE number 5833832