Integrability of a linear center perturbed by a fifth degree homogeneous polynomial
type: Item
instance of: scholarly article
title: Integrability of a linear center perturbed by a fifth degree homogeneous polynomial
zbMATH Open document ID: 0897.34030
DOI: 10.5565/PUBLMAT_41297_02
author: Javier Chavarriga
author: Jaume Giné
published in: Publicacions Matemàtiques
publication date: 1998-10-25T00:00:00Z
full work available at URL: https://eudml.org/doc/41322
review text: The authors study the integrability of planar polynomial differential systems: \[ \dot x= -y+ X_5(t,y),\quad \dot y= x+ Y_5(x, y),\tag{1} \] where \(X_5\) and \(Y_5\) are homogeneous polynomials of \(x\) and \(y\) with constant coefficients. They obtain four sets of complicated conditions for (1) to be integrable. They give a conjecture for the vanishing of all Lyapunov constants, i.e., the angular parameters and the radial ones must be independent. If this conjecture is true, then the integrable cases found by them will be the only possible ones.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34A05
zbMATH DE Number: 1146187
zbMATH Keywords: center
zbMATH Keywords: integrability
zbMATH Keywords: planar polynomial differential systems
zbMATH Keywords: Lyapunov constants
reviewed by: Yanqian Ye
MaRDI profile type: Publication
OpenAlex ID: W2044763069
description: scientific article; zbMATH DE number 1146187