Isochronous centers and isochronous functions
type: Item
instance of: scholarly article
title: Isochronous centers and isochronous functions
zbMATH Open document ID: 1028.34034
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2003-06-18T00:00:00Z
review text: The author investigates the isochronous centers of two classes of planar systems of ordinary differential equations: 1) Liénard systems of the form \((\dot x)=y-F(x),(\dot y)=-g(x)\), 2) Hamiltonian systems of the form \((\dot x)=-g(y)\), \((\dot y)=f(x)\), with emphasis on the case when the functions \(g\) or \(f\) are isochronous. For the first class of systems with a center at the origin, the author proves that, if \(g\) is isochronous, then the center is isochronous if and only if \(F\equiv 0\). For the second class of systems with a center at the origin, the author proves that if \(f\) or \(g\) is isochronous, then the center is isochronous if and only if the other is also isochronous.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1885875
zbMATH Keywords: Liénard systems
zbMATH Keywords: Hamiltonian systems
author: Li-Jun Yang
MaRDI profile type: Publication
full work available at URL: s102550200031
OpenAlex ID: W2065346514
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DOI: 10.1007/S102550200031
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description: scientific article; zbMATH DE number 1885875