Cyclicity versus center problem
type: Item
instance of: scholarly article
title: Cyclicity versus center problem
zbMATH Open document ID: 1210.34049
author: Armengol Gasull
author: Jaume Giné
published in: Qualitative Theory of Dynamical Systems
publication date: 2010-12-14T00:00:00Z
review text: The authors consider a one-parameter family of differential systems of the form \[ \begin{aligned} \dot x &=-y+ a^k x(x^2+ y^2)+ aP(x,y,a),\\ \dot y &=x+ a^ky(x^2+ y^2)+ aQ(x,y,a),\end{aligned} \] where \(P\) and \(Q\) are analytic functions, starting at least with terms of degree 4 in \(x\) and \(y\), and \(k\geq 1\) is an integer number. It is proved that the cyclicity of the origin is at most \(k- 1\) and there are analytic functions, \(P\) and \(Q\), for which this upper bound is sharp.
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37C27
zbMATH DE Number: 5826160
zbMATH Keywords: polynomial differential system
zbMATH Keywords: focal quantities
zbMATH Keywords: Lyapunov constants
zbMATH Keywords: cyclicity
zbMATH Keywords: limit cycles
reviewed by: A. P. Sadovskiĭ
MaRDI profile type: Publication
full work available at URL: s12346-010-0022-9
OpenAlex ID: W2038985136
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DOI: 10.1007/S12346-010-0022-9
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description: scientific article; zbMATH DE number 5826160