Strongly isochronous centers of cubic systems with degenerate infinity
type: Item
instance of: scholarly article
title: Strongly isochronous centers of cubic systems with degenerate infinity
zbMATH Open document ID: 1316.34030
DOI: 10.1134/S001226611407012X
published in: Differential Equations
publication date: 2014-12-17T00:00:00Z
review text: Consider the planar system \[ \dot{x}=-y-P(x,y),\, \dot{y}=x+Q(x,y), \] where \(P\) and \(Q\) are holomorphic in a neighborhood of the origin and with no constant or linear terms. The system is strongly isochronous of order \(n\) if all representation points at \(t_{0}\) on the rays \(I_{\nu}\), \(\nu=1,2,\dots,n\), and starting to move at times \(t_{0}\) along the trajectories of a center or a focus successively pass from one of these rays to another in the same time \(T=\frac{2 \pi}{n}\). The author considers the case in which \(P\) and \(Q\) contain only quadratic and cubic terms. It is shown that this system can have a strongly isochronous center of order two only. All second order strongly isochronous systems are given.
reviewed by: M. A. M. Alwash
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C08
zbMATH DE Number: 6381336
zbMATH Keywords: center
zbMATH Keywords: planar system
zbMATH Keywords: isochronous centers
author: Dijana Dolićanin-Djekić
MaRDI profile type: Publication
cites work: Q4246492
cites work: Strong isochronism of polynomial reversible dynamical systems on the plane with homogeneous nonlinearities of degree 4
cites work: Strong isochronism of two-dimensional reversible cubic systems
cites work: Quadratic-like cubic systems
cites work: Isochronous centers of cubic systems with degenerate infinity
cites work: Isochronous and strongly isochronous oscillations of two-dimensional monodromic holomorphic dynamical systems
full work available at URL: s001226611407012x
OpenAlex ID: W2086077463
description: scientific article; zbMATH DE number 6381336