Centers of quadratic systems
type: Item
instance of: scholarly article
title: Centers of quadratic systems
zbMATH Open document ID: 0685.34024
author: Roberto Conti
published in: Ricerche di Matematica
publication date: 1987-01-01T00:00:00Z
review text: A quadratic system in the autonomous system \(\dot x=P(x,y)\), \(\dot y=Q(x,y)\), where \[ P(x,y)=\sum^{2}_{j+\ell =0}a_{j,\ell}x^ jy^{\ell},\quad Q(x,y)=\sum^{2}_{j+\ell =0}b_{j,\ell}x^ jy^{\ell} \] are relatively prime real polynomials of degree at most two which are not both linear. A singular point S of the system is a center when there is a neighbourhood of S entirely covered by cycles. Let \(N_ S\) be the union of the interior regions of the cycles surrounding S. The author shows that there are only five topologically different types of \(N_ S\), and that there are only four possible combinations of \(N_ S\) for a system.
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 4122364
zbMATH Keywords: quadratic systems
zbMATH Keywords: centers
zbMATH Keywords: autonomous system
zbMATH Keywords: cycles
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4122364