Linearizability conditions of time-reversible quartic systems having homogeneous nonlinearities
type: Item
instance of: scholarly article
title: Linearizability conditions of time-reversible quartic systems having homogeneous nonlinearities
zbMATH Open document ID: 1159.34025
author: Xingwu Chen
author: Valery G. Romanovski
author: Weinian Zhang
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2008-08-27T00:00:00Z
review text: This paper gives necessary and sufficient conditions that a polynomial system \[ \dot x = x + P(x,y), \qquad \dot y = -y + Q(x,y) \] on \(\mathbb{C}^2\) that is time-reversible be linearizable, in the case that the nonlinear terms are homogeneous quartic polynomials in \(x\) and \(y\). The author's method is to compute an initial string of the so-called linearizability quantities, find the irreducible decomposition of the complex variety that they generate, and then show that a system corresponding to an element of each component in a component is linearizable, typically using the method of Darboux linearization. Based on these results the authors also characterize when centers of corresponding real systems are isochronous.
reviewed by: Douglas S. Shafer
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C20
zbMATH DE Number: 5316885
zbMATH Keywords: linearizability
zbMATH Keywords: time-reversibility
zbMATH Keywords: center
zbMATH Keywords: isochronicity
MaRDI profile type: Publication
full work available at URL: j.na.2007.07.009
OpenAlex ID: W2003004883
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DOI: 10.1016/J.NA.2007.07.009
description: scientific article; zbMATH DE number 5316885