The generalized center problem of degenerate resonant singular point
type: Item
instance of: scholarly article
title: The generalized center problem of degenerate resonant singular point
zbMATH Open document ID: 1159.34027
author: Qi Zhang
author: Gui Weihua
author: Yirong Liu
published in: Bulletin des Sciences Mathématiques
publication date: 2009-03-11T00:00:00Z
review text: The paper is concerned with generalized center condition and integrability of the origin for complex polynomial differential equation system \[ \left\{ \begin{aligned} \frac{dz}{dT}&=pz^{n+1}w^n+ \sum_{\alpha+\beta=2n+2}^{\infty}a_{\alpha\beta}z^{\alpha}w^{\beta},\\ \frac{dw}{dT}&=-qw^{n+1}z^n- \sum_{\alpha+\beta=2n+2}^{\infty}b_{\alpha\beta}z^{\alpha}w^{\beta},\\ \end{aligned} \right. \eqno (1) \] where \(z\), \(w\), \(T\) are complex, \(a_{\alpha\beta}\), \(b_{\alpha\beta}\) are comlex constants, \(p,q\in\mathbb Z^{+}\), \((p,q)=1\), \(n\) is a positive integer. The origin is a degenerate \(p:-q\) resonant singular point of system (1). The method based on a homeomorphic transformation of the degenerate singular point into the elementary one allows to compute the generalized singular point quantities and determine the generalized center condition for the origin. Necessary and sufficient conditions of generalized complex center of degenerate resonant singular point are obtained.
reviewed by: Eugene Ershov
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 5527927
zbMATH Keywords: generalized center condition
zbMATH Keywords: integrability
zbMATH Keywords: degenerate resonant singular point
MaRDI profile type: Publication
full work available at URL: j.bulsci.2007.10.003
OpenAlex ID: W2001626398
cites work: Q4715040
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DOI: 10.1016/J.BULSCI.2007.10.003
description: scientific article; zbMATH DE number 5527927