Elliptic limit cycles of two-dimensional autonomous differential systems
type: Item
instance of: scholarly article
title: Elliptic limit cycles of two-dimensional autonomous differential systems
zbMATH Open document ID: 1043.34027
DOI: 10.1023/A:1022310410920
author: M. V. Dolov
author: Yu. V. Pavlyuk
published in: Differential Equations
publication date: 2003-05-25T00:00:00Z
review text: The authors consider the polynomial system \[ dx/dt = P(x,y),\quad dy/dt = Q(x,y),\tag{1} \] where the maximum \(n\) of the degrees of \(P,Q\) is at least 2, and study the problem of estimating the number of elliptic (or circular) limit cycles of (1). The main result is that there exist such systems (1) with \(n=4\) having 3 circular limit cycles with distinct centers lying on the same straight line. This shows a wrong assertion on circular limit cycles of (1) if \(n\) is even in the paper [\textit{N. Sadovskaia} and \textit{R. Ramires}, Tech. Report MA 2-IR-99-00015 (Version 2), Univ. Politech. de Cataluna (in Spanish)]
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 1916187
zbMATH Keywords: algebraic limit cycles
zbMATH Keywords: \(n\)th-degree polynomial systems
reviewed by: Jinghuang Tian
MaRDI profile type: Publication
full work available at URL: a:1022310410920
OpenAlex ID: W83706924
description: scientific article; zbMATH DE number 1916187