Saddle values and integrability conditions of quadratic differential systems
type: Item
instance of: scholarly article
title: Saddle values and integrability conditions of quadratic differential systems
zbMATH Open document ID: 0659.34051
published in: Chinese Annals of Mathematics. Series B
publication date: 1987-01-01T00:00:00Z
review text: The first three saddle values of weak saddle of quadratic differential system (QDE) are computed with Poincaré's method. In order to do this, two theorems are given. The Theorem 1 about the perturbation of a system was used to derive the Theorem 2 which gives the formulae of the three saddle values \(R_ 1,R_ 2,R_ 3\). The necessary and sufficient condition of integrability of the given system, whether real or complex, is \(R_ 1=R_ 2=R_ 3=0\). This conclusion was proved by applying the method and results of Dulac that was published in Bull. Soc. Math. 32, 230-252 (1908). The formulae of focal values for the real quadratic differential equations and a new proof of the famous Bautin's result may be derived by the method given in this paper.
Mathematics Subject Classification ID: 34C40
Mathematics Subject Classification ID: 34D10
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 37G15
zbMATH DE Number: 4077766
zbMATH Keywords: saddle values
zbMATH Keywords: weak saddle of quadratic differential system
zbMATH Keywords: Poincaré's method
author: Deming Zhu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4077766