Stable manifolds for impulsive equations under nonuniform hyperbolicity
type: Item
instance of: scholarly article
title: Stable manifolds for impulsive equations under nonuniform hyperbolicity
zbMATH Open document ID: 1216.34037
author: Luís Barreira
author: Claudia Valls
published in: Journal of Dynamics and Differential Equations
publication date: 2011-01-07T00:00:00Z
review text: The authors construct invariant stable manifolds for impulsive differential equations under sufficiently small perturbations of a linear equation. Compared with former work, there are two novelties: one is that the authors consider the general case of perturbations of nonuniform exponential dichotomies; and the other is that the authors obtain the optimal smoothness of the invariant outside the jumping times. The novelty of the proof is the use of the fiber contraction principle to establish the smoothness of the invariant manifolds. The reviewer thinks that this is an excellent contribution to the topic of stable manifolds for impulsive equations.
Mathematics Subject Classification ID: 34C45
Mathematics Subject Classification ID: 34D09
Mathematics Subject Classification ID: 34D10
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5833829
zbMATH Keywords: impulsive equations
zbMATH Keywords: nonuniform exponential dichotomies
zbMATH Keywords: stable manifolds impulsive equations
zbMATH Keywords: stable manifolds
reviewed by: Fulai Chen
MaRDI profile type: Publication
full work available at URL: s10884-010-9161-6
OpenAlex ID: W2019061992
cites work: Stability of nonautonomous differential equations
cites work: Q3995625
cites work: Q5646734
cites work: FAMILIES OF INVARIANT MANIFOLDS CORRESPONDING TO NONZERO CHARACTERISTIC EXPONENTS
cites work: Q4853771
DOI: 10.1007/S10884-010-9161-6
description: scientific article; zbMATH DE number 5833829