Characterization of stable manifolds for nonuniform exponential dichotomies
type: Item
instance of: scholarly article
title: Characterization of stable manifolds for nonuniform exponential dichotomies
zbMATH Open document ID: 1157.37012
author: Luís Barreira
author: Claudia Valls
published in: Discrete and Continuous Dynamical Systems
publication date: 2008-08-22T00:00:00Z
review text: With the aim to study perturbations of linear differential equation \(v'=A(t)\) (\(A(t)\) is a \(C^1\) function) that admit a nonuniform exponential dichotomy at sufficiently small \(C^1\) perturbation \(f(t,v)\) with bounded Lipschitz derivative the authors establish the following results for the perturbed equation: 1) the existence of \(C^1\) stable manifolds, 2) the exponential decay of the derivative of the flow defined by the autonomous equation \(t'=1, v'=A(t)v+f(t,v)\) along the stable manifold, in addition to the expected exponential decay of the flow along the stable manifold, 3) a characterization of the stable manifold as the set of points whose trajectories have a controlled exponential growth rate, namely those whose exponential growth rate is sufficiently far away from the positive Lyapounov exponents of the exponential dichotomy.
reviewed by: Irina V. Konopleva
Mathematics Subject Classification ID: 37D10
Mathematics Subject Classification ID: 34D09
Mathematics Subject Classification ID: 34D10
zbMATH DE Number: 5315189
zbMATH Keywords: nonuniform exponential dichotomies
zbMATH Keywords: stable manifolds
MaRDI profile type: Publication
full work available at URL: dcds.2008.21.1025
OpenAlex ID: W2325497759
DOI: 10.3934/DCDS.2008.21.1025
description: scientific article; zbMATH DE number 5315189