The cyclicity of the period annulus of the quadratic Hamiltonian systems with non-Morsean point
type: Item
instance of: scholarly article
title: The cyclicity of the period annulus of the quadratic Hamiltonian systems with non-Morsean point
zbMATH Open document ID: 0960.37027
author: Yulin Zhao
author: Zhaojun Liang
author: Gang Lü
published in: Journal of Differential Equations
publication date: 2000-04-27T00:00:00Z
review text: This paper deals with the number of limit cycles for small quadratic perturbations of quadratic Hamiltonian systems with non-Morsean point, that is \[ \begin{aligned} \dot x&= 2xy+ \varepsilon \Bigl( \sum_{i+j\leq 2} a_{ij} (\varepsilon) x^i y^j\Bigr),\\ \dot y&= 6x+ 6x^2- y^2+ \varepsilon \Bigl( \sum_{i+j\leq 2} b_{ij} (\varepsilon) x^i y^j \Bigr), \end{aligned} \tag \(1_\varepsilon\) \] where \(a_{ij} (\varepsilon)\) and \(b_{ij} (\varepsilon)\) depend analytically on the small parameter \(\varepsilon\). The authors prove that, for small \(\varepsilon\), the maximum number of limit cycles in \((1)_\varepsilon\) which emerge from the period annulus is equal to two.
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 37G15
zbMATH DE Number: 1437343
zbMATH Keywords: quadratic Hamiltonian
zbMATH Keywords: perturbation
zbMATH Keywords: non-Morsean point
zbMATH Keywords: limit cycles
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: jdeq.1999.3704
OpenAlex ID: W2027814307
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DOI: 10.1006/JDEQ.1999.3704
description: scientific article; zbMATH DE number 1437343