On the number of critical periods for planar polynomial systems
type: Item
instance of: scholarly article
title: On the number of critical periods for planar polynomial systems
zbMATH Open document ID: 1157.34021
author: Anna Cima
author: Armengol Gasull
author: Paulo R. da Silva
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2008-09-10T00:00:00Z
review text: The authors consider planar polynomial systems and get some lower bounds of critical periods for families of centers which are perturbations of the linear one. They present a method which lets them prove that there are polynomial centers of degree \(l\) with at least \(2[(l-2)/2]\) critical periods, moreover they study concrete families of potential, reversible, and Liénard centers. The last case is studied in more detail; in particular, it is proved that the number of critical periods obtained with the authors' approach does not increase with the order of the perturbation.
reviewed by: Valery A. Gaiko
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34E10
zbMATH DE Number: 5324166
zbMATH Keywords: planar polynomial system
zbMATH Keywords: potential system
zbMATH Keywords: period function
zbMATH Keywords: critical period
zbMATH Keywords: perturbation
zbMATH Keywords: reversible center
zbMATH Keywords: Hamiltonian center
zbMATH Keywords: Liénard center
MaRDI profile type: Publication
full work available at URL: j.na.2007.07.031
OpenAlex ID: W2099969983
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DOI: 10.1016/J.NA.2007.07.031
description: scientific article; zbMATH DE number 5324166