Medium amplitude limit cycles in second order perturbed polynomial Liénard systems
type: Item
instance of: scholarly article
title: Medium amplitude limit cycles in second order perturbed polynomial Liénard systems
zbMATH Open document ID: 1426.34043
author: Salomón Rebollo-Perdomo
author: Vanessa Salas-Mendoza
published in: Journal of Mathematical Analysis and Applications
publication date: 2019-03-21T00:00:00Z
review text: The paper is devoted to polynomial generalized Liénard systems as a result of second order polynomial perturbations of a Hamiltonian system with a linear center. The main purpose is to derive an upper bound for medium (amplitude) limit cycles of this system that is, limit cycles that bifurcate from some closed orbits of the Hamiltonian system. The authors find a generic (open and dense) subset in the space of perturbations of degree \(2l\), with \(l\geq1\), such that each associated perturbed generalized Liénard system has at most \(2l-1\) medium limit cycles. They show that this upper bound is reached and finally present some concrete examples. The proof of this result is based on the study of higher order Poincaré-Pontryagin-Melnikov functions of the displacement function associated with the Liénard system.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34E10
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 37J40
zbMATH DE Number: 7040425
zbMATH Keywords: limit cycle
zbMATH Keywords: Liénard system
zbMATH Keywords: abelian integral
zbMATH Keywords: perturbed Hamiltonian system
MaRDI profile type: Publication
full work available at URL: j.jmaa.2018.12.079
OpenAlex ID: W2909719005
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DOI: 10.1016/J.JMAA.2018.12.079
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description: scientific article; zbMATH DE number 7040425