Local bifurcation of critical periods for a class of Liénard equations
type: Item
instance of: scholarly article
title: Local bifurcation of critical periods for a class of Liénard equations
zbMATH Open document ID: 1359.34041
author: Yi Shao
author: Chun-Xiang A
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2014-12-09T00:00:00Z
review text: Consider the planar system \[ {dx\over dt}= y,\quad {dy\over dt}= -x+ \sum^n_{i=1} a_{2i} x^{2i}\tag{\(*\)} \] with \(a= (a_2,a_4,\dots, a_{2n})\in\mathbb{R}^n\), \(a_{2n}\neq 0\), having the origin as center equilibrium. The authors prove that to any \(a_{2n}\neq 0\) there is \(\delta(a_{2n})> 0\) such that for all \(a\) with \(|a|<\delta(a_{2n})\) system \((*)\) has at most \(2n-2\) critical periods near the origin (taken into account their multiplicities). Moreover, they prove that to any small \(\delta\) there is a vector \(a\) with \(|a|<\delta\) such that \((*)\) has \(2n-2\) critical periods near the origin.
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C14
zbMATH DE Number: 6378533
zbMATH Keywords: period function
zbMATH Keywords: critical periods
zbMATH Keywords: local bifurcation
MaRDI profile type: Publication
full work available at URL: s10255-014-0407-7
OpenAlex ID: W2396692279
cites work: On the monotonicity of the period function of a quadratic system
cites work: The monotonicity of the period function for planar Hamiltonian vector fields
cites work: Finiteness for critical periods of planar analytic vector fields
cites work: Bifurcation of Critical Periods for Plane Vector Fields
cites work: The period function of a Hamiltonian quadratic system
cites work: The period function of classical Liénard equations
cites work: Bifurcation of critical periods from the rigid quadratic isochronous vector field
cites work: The bifurcation set of the period function of the dehomogenized Loud's centers is bounded
cites work: The period function of reversible quadratic centers
cites work: The monotonicity of period function for the codimension four quadratic system \(Q_4\).
cites work: Quadratic systems with center and their perturbations
DOI: 10.1007/S10255-014-0407-7
description: scientific article; zbMATH DE number 6378533