Ordinary dichotomy and global linearization
type: Item
instance of: scholarly article
title: Ordinary dichotomy and global linearization
zbMATH Open document ID: 1163.34363
author: Liangping Jiang
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-03-25T00:00:00Z
review text: The author finds sufficient conditions for the topological equivalence between the nonautonomous equation \[ x'= A(t)x+ f(t,x)\qquad (x\in\mathbb{R}^n)\tag{1} \] and its linear system \[ x'= A(t)x.\tag{2} \] That means the existence of a homeomorphism \(H(t,\cdot)\) of \(\mathbb{R}^n\) into \(\mathbb{R}^n\) such: (i) \(H(t,x)\to x\) is bounded in \(\mathbb{R}\times \mathbb{R}^n\), (ii) if \(x(t)\) is a solution of (1) then \(H(t,x(t))\) is a solution of (2).
reviewed by: S. Kostadinov
Mathematics Subject Classification ID: 34D09
Mathematics Subject Classification ID: 34D10
Mathematics Subject Classification ID: 34C41
zbMATH DE Number: 5532919
zbMATH Keywords: ordinary dichotomy
zbMATH Keywords: (strongly)topologically equivalent
zbMATH Keywords: (strongly)equivalent function
MaRDI profile type: Publication
full work available at URL: j.na.2008.03.060
OpenAlex ID: W2037707083
cites work: A generalization of Hartman's linearization theorem
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cites work: Dichotomies in stability theory
DOI: 10.1016/J.NA.2008.03.060
description: scientific article; zbMATH DE number 5532919