On the number of limit cycles in double homoclinic bifurcations
type: Item
instance of: scholarly article
title: On the number of limit cycles in double homoclinic bifurcations
zbMATH Open document ID: 1013.34026
DOI: 10.1007/BF02879797
author: Jian Chen
author: Maoan Han
published in: Science in China. Series A
publication date: 2002-08-15T00:00:00Z
review text: The authors consider perturbations of Hamiltonian systems in \(\mathbb{R}^2\). They assume that the unperturbed system possesses a double homoclinic loop (figure-eight-configuration) at a hyperbolic fixed point. The main results concern the maximal number of limit cycles near the given homoclinic orbits. The condition permitting the existence of the limit cycles are formulated in terms of Melnikov functions.
reviewed by: Jürgen Knobloch
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 1782027
zbMATH Keywords: homoclinic orbits
zbMATH Keywords: limit cycles
zbMATH Keywords: bifurcation
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02879797
OpenAlex ID: W2224899793
description: scientific article; zbMATH DE number 1782027