Classification of the centers, of their cyclicity and isochronicity for two classes of generalized quintic polynomial differential systems
type: Item
instance of: scholarly article
title: Classification of the centers, of their cyclicity and isochronicity for two classes of generalized quintic polynomial differential systems
zbMATH Open document ID: 1195.34046
author: Jaume Llibre
author: Claudia Valls
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2009-11-23T00:00:00Z
review text: This article deals with the center-focus problem for a class of polynomial differential systems in \({\mathbb{R}^2}\) of degree \(d\) that in complex notation \(z = x + iy\) can be written as \[ \dot z = (\lambda+i) z + (z \overline{z})^{\frac{d-5}{2}} \left(A z^{4+j} \overline{z}^{1-j} + B z^3 \overline{z}^2 + C z^{2-j} \overline{z}^{3+j}+D \overline{z}^5\right), \] where \(j\) is either 0 or 1, \(d\) is an arbitrary odd positive integer greater than or equal to five, \({\lambda \in \mathbb{R}}\), and \({A,B,C,D \in \mathbb{C}}\). The authors are mainly interested in finding new families of centers of such a systems as well as in studying their cyclicity and isochronicity.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 5636894
zbMATH Keywords: polynomial vector field
zbMATH Keywords: center-focus problem
zbMATH Keywords: center
zbMATH Keywords: isochronous center
zbMATH Keywords: cyclicity
MaRDI profile type: Publication
full work available at URL: s00030-009-0029-6
OpenAlex ID: W2053710615
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DOI: 10.1007/S00030-009-0029-6
description: scientific article; zbMATH DE number 5636894