Center conditions and integrable forms for the Poincaré problem
type: Item
instance of: scholarly article
title: Center conditions and integrable forms for the Poincaré problem
zbMATH Open document ID: 1323.34043
author: Gary R. Nicklason
published in: Journal of Mathematical Analysis and Applications
publication date: 2015-03-27T00:00:00Z
review text: The polynomial system \[ {dx\over dt}=-y-p(x,y),\quad {dy\over dt}=x+q(x,y), \] where \(p\), \(q\) are homogeneous polynomials of degree \(n\geq 2\) is considered. Several sets of center conditions valid for general values of \(n\) are obtained by finding integrable forms of the system. A general class of centers valid for even values of \(n\) which is based on certain parity properties of a related differential equation is also found and several conditions which are valid for \(n=4,5\) are given.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34A05
zbMATH DE Number: 6420033
zbMATH Keywords: center focus problem
zbMATH Keywords: integrable systems
zbMATH Keywords: Abel differential equation
zbMATH Keywords: symmetric centers
reviewed by: A. P. Sadovskiĭ
MaRDI profile type: Publication
full work available at URL: j.jmaa.2013.06.072
OpenAlex ID: W2007016375
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DOI: 10.1016/J.JMAA.2013.06.072
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description: scientific article; zbMATH DE number 6420033