Computing center conditions for vector fields with constant angular speed
type: Item
instance of: scholarly article
title: Computing center conditions for vector fields with constant angular speed
zbMATH Open document ID: 1032.34026
DOI: 10.1016/S0377-0427(02)00818-X
published in: Journal of Computational and Applied Mathematics
publication date: 2003-05-22T00:00:00Z
review text: The authors study the planar analytic system \[ dx/dt = -y + xH(x,y), \qquad dy/dt= x+yH(x,y), \tag{1} \] where \(H\) is analytic and \(H(0,0)= 0\). Conditions are obtained to characterize the center at the origin of (1). The equivalence between those conditions and the vanishing of the coefficients of the radial component of the normal form is proved. A recursive algorithm of coefficient conditions is found for the \((0,0)\) to be a center. A few subfamilies having a center are given. The centers of quartic polynomial systems and of two other families are derivated to determine the maximum number of limit cycles which can bifurcate from a fine focus.
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 1915270
zbMATH Keywords: Centers
zbMATH Keywords: fine focus
zbMATH Keywords: limit cycles
zbMATH Keywords: periodic orbits
zbMATH Keywords: planar analytic systems
author: Antonio Algaba
author: M. Reyes
reviewed by: Jinghuang Tian
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1915270