Perturbations of quadratic Hamiltonian systems with symmetry
type: Item
instance of: scholarly article
title: Perturbations of quadratic Hamiltonian systems with symmetry
zbMATH Open document ID: 0854.34035
DOI: 10.1016/S0294-1449(16)30096-8
author: Iliya D. Iliev
author: Emil Horozov
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1997-01-22T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78374
review text: The main result of the paper is the following Theorem 1. Let \(H\) be a generic cubic Hamiltonian with a centroid symmetry: \(H(- x, - y)= - H(x, y)\). Then any quadratic perturbation of the corresponding Hamiltonian system \(\dot x= H_y+ \varepsilon f(x, y)\), \(\dot y= - H_x+ \varepsilon g(x, y)\) has at most two limit cycles for \(\varepsilon\) small enough. The technique used is based essentially on the notion and on the properties of the centroid curve formed by the mass centres of a continuous family of ovals within the level curves of \(H\).
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34D10
zbMATH DE Number: 873773
zbMATH Keywords: cubic Hamiltonian
zbMATH Keywords: centroid symmetry
zbMATH Keywords: quadratic perturbation
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: two limit cycles
reviewed by: Yuriy V. Rogovchenko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 873773