Poincaré type theorems for non-autonomous systems
type: Item
instance of: scholarly article
title: Poincaré type theorems for non-autonomous systems
zbMATH Open document ID: 1184.34005
author: Hao Wu
author: Weigu Li
published in: Journal of Differential Equations
publication date: 2008-11-12T00:00:00Z
review text: The authors develop a theory of normal forms for the case of nonautonomous systems of differential equations. Consider an analytic system of differential equations \[ x'=F(x,t)=A(t)x+f(x,t), \tag{1} \] where \(f=O(\|x\|^2)\), and its linearization, \[ x'=A(t)x. \] In terms of the Sacker-Sell spectrum of the linearization, they give conditions under which (i) any system \[ x'=G(x,t) \] with \(G-f=O(\|x\|^d)\) is locally analytically equivalent to (1) (equivalence in the jet class); (ii) system (1) is locally analytically equivalent to its linearization (Poincaré type); (iii) system (1) is locally analytically equivalent to a system \[ x'=A(t)x+g(x,t), \] where \(g\) is a polynomial in \(x\) (Poincaré-Dulac type).
reviewed by: Sergei Yu. Pilyugin
Mathematics Subject Classification ID: 34-02
Mathematics Subject Classification ID: 34C41
zbMATH DE Number: 5365158
zbMATH Keywords: normal form
zbMATH Keywords: non-autonomous differential system
zbMATH Keywords: Poincaré theorem
MaRDI profile type: Publication
full work available at URL: j.jde.2008.05.005
OpenAlex ID: W2019297309
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DOI: 10.1016/J.JDE.2008.05.005
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description: scientific article; zbMATH DE number 5365158