The problem of the centre for cubic systems with two parallel invariant straight lines and one invariant conic
type: Item
instance of: scholarly article
title: The problem of the centre for cubic systems with two parallel invariant straight lines and one invariant conic
zbMATH Open document ID: 1190.34032
author: Dumitru Cozma
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2009-06-08T00:00:00Z
review text: For the cubic differential system \[ \begin{aligned} \dot x &= y+ ax^2+ cxy+ fy^2+ kx^3+ mx^2y+ pxy^2+ ry^3,\\ \dot y &= -(x+ gx^2+ dxy+ by^2+ sx^3+ gx^2y+ nxy^2+ ly^3)\end{aligned} \] with two parallel invariant straight lines and at least one invariant conic it is proved that a singular point with pure imaginary eigenvalues is a center if and only if the first three Lyapunov quantities \(L_j\), \(j= 1,2,3\), vanish.
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 5562674
zbMATH Keywords: cubic differential systems
zbMATH Keywords: center-focus problem
zbMATH Keywords: invariant algebraic curves
zbMATH Keywords: integrability
reviewed by: A. P. Sadovskiĭ
MaRDI profile type: Publication
full work available at URL: s00030-008-7044-x
OpenAlex ID: W2032448933
DOI: 10.1007/S00030-008-7044-X
description: scientific article; zbMATH DE number 5562674