Planar real polynomial differential systems of degree \(n> 3\) having a weak focus of high order
type: Item
instance of: scholarly article
title: Planar real polynomial differential systems of degree \(n> 3\) having a weak focus of high order
zbMATH Open document ID: 1254.34048
DOI: 10.1216/RMJ-2012-42-2-657
author: Jaume Llibre
author: Roland Rabanal
published in: Rocky Mountain Journal of Mathematics
publication date: 2012-05-16T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmjm/1335187172
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C07
zbMATH DE Number: 6035457
zbMATH Keywords: weak focus
zbMATH Keywords: center
zbMATH Keywords: polynomial vector fields
MaRDI profile type: Publication
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review text: The authors construct polynomial systems of degree \(n>3\), which for even \(n\) have a week focus of order \(n^2-1\) and for odd \(n\) have a week focus of order \((n^2-1)/2\) at the origin. The systems are from the family of the form NEWLINE\[NEWLINE \dot x=-y(1-f_\alpha(x,y))+P(x,y), \;\dot y=x(1-f_\alpha(x,y))+Q(x,y), NEWLINE\]NEWLINE where \( f_\alpha(x,y) \) is a real homogeneous polynomial of degree \(n-1\) depending on the real parameter \(\alpha\), \(P\) and \(Q\) are homogeneous polynomials of degree \(n\) with small real coefficients. The obtained result improves previously known estimates.
description: scientific article; zbMATH DE number 6035457