Center and isochronous center problems for quasi analytic systems
type: Item
instance of: scholarly article
title: Center and isochronous center problems for quasi analytic systems
zbMATH Open document ID: 1169.34029
author: Jibin Li
author: Yirong Liu
publication date: 2008-09-12T00:00:00Z
review text: Consider the planar quasi-analytic systems \[ \begin{aligned} {dx\over dt} &=\delta x- y+ \sum^\infty_{k=2} (x^2+ y^2)^{(k-1)(\lambda- 1)/2}X_k(x,y),\\ {dy\over dt} &= x+\delta y+ \sum^\infty_{k=2} (x^2+ y^2)^{(k-1)(\lambda- 1)/2} Y_k(x, y),\end{aligned} \] where \[ \begin{aligned} X_k(x, y) &= \sum_{\alpha+\beta= k} A_{\alpha\beta} x^\alpha y^\beta,\\ Y_k(x, y) &= \sum_{\alpha+\beta= k} B_{\alpha\beta} x^\alpha y^\beta,\end{aligned} \] \(\lambda\) is a real constant and \(\lambda\neq 0\). Two recursive formulas to determine the focal values and period constants are given. Using general results on quasi-quadratic systems, the problem of an isochronous center of the origin is completely solved.
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 5343499
zbMATH Keywords: generalized focal value
zbMATH Keywords: center integral
zbMATH Keywords: periodic constant
zbMATH Keywords: isochronous center
zbMATH Keywords: quasi-analytic planar differential system
reviewed by: A. P. Sadovskiĭ
MaRDI profile type: Publication
full work available at URL: s10114-008-6701-7
OpenAlex ID: W1992258607
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DOI: 10.1007/S10114-008-6701-7
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5343499