The cyclicity of period annuli for a class of cubic Hamiltonian systems with nilpotent singular points
type: Item
instance of: scholarly article
title: The cyclicity of period annuli for a class of cubic Hamiltonian systems with nilpotent singular points
zbMATH Open document ID: 1411.34047
author: Jihua Yang
author: Liqin Zhao
published in: Journal of Differential Equations
publication date: 2018-10-02T00:00:00Z
review text: In the paper, the authors investigate the maximal number of limit cycles that might occur in a class of symmetric cubic Hamiltonian systems with a nilpotent singular point under polynomial perturbations. It is well-known that the number of zeros of the abelian integral provides an upper bound for the number of limit cycles of such systems. They first obtain the algebraic structure of the abelian integral in terms of nine generators. Then, three Picard-Fuchs equations satisfied by the generators are derived. From the existence of a second-order differential operator that acts on the abelian integral, the number of zeros of the abelian integral can be estimated. The number of limit cycles follows from the Poincaré-Pontryagin Theorem.
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34E10
zbMATH DE Number: 6946020
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: abelian integral
zbMATH Keywords: weakened Hilbert's 16th problem
zbMATH Keywords: Picard-Fuchs equation
zbMATH Keywords: Chebyshev space
reviewed by: Kwok-wai Chung
MaRDI profile type: Publication
full work available at URL: j.jde.2017.06.027
OpenAlex ID: W2726863439
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DOI: 10.1016/J.JDE.2017.06.027
description: scientific article; zbMATH DE number 6946020