Theory of center-focus for a class of higher-degree critical points and infinite points
type: Item
instance of: scholarly article
title: Theory of center-focus for a class of higher-degree critical points and infinite points
zbMATH Open document ID: 1012.34027
DOI: 10.1007/BF02878718
published in: Science in China. Series A
publication date: 2002-08-15T00:00:00Z
review text: Here, the real planar autonomous differential systems with higher-degree critical points (including elementary critical points and infinite points) \[ \frac{dx}{dt}=\sum_{k=2n+1}^{\infty}X_{k}(x,y)=X(x,y),\quad \frac{dy}{dt}=\sum_{k=2n+1}^{\infty}Y_{k}(x,y)=Y(x,y), \] and \[ \frac{dx}{dt}=\sum_{k=0}^{2n+1}X_{k}(x,y),\quad \frac{dy}{dt}=\sum_{k=0}^{2n+1}Y_{k}(x,y), \] are studied, where \(X_{k}(x,y), Y_{k}(x,y)\) are homogeneous polynomials of degree \(k\) and the functions \(X(x,y), Y(x,y)\) are analytic at the origin. The results extend statements concerning the detection of center or focus, successor function, central integration, integration factor, focal values, values of singular points and bifurcation of limit cycles.
reviewed by: Ladislav Adamec
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 37G15
zbMATH DE Number: 1782095
zbMATH Keywords: higher-degree critical infinite points
zbMATH Keywords: center-focus
zbMATH Keywords: bifurcation of limit cycles
author: Yirong Liu
MaRDI profile type: Publication
cites work: Q4715040
cites work: Theory of values of singular point in complex autonomous differential systems
full work available at URL: https://doi.org/10.1007/bf02878718
OpenAlex ID: W1557619183
description: scientific article; zbMATH DE number 1782095