Perturbation of a period annulus bounded by a heteroclinic loop connecting two hyperbolic saddles
type: Item
instance of: scholarly article
title: Perturbation of a period annulus bounded by a heteroclinic loop connecting two hyperbolic saddles
zbMATH Open document ID: 1385.37077
published in: Qualitative Theory of Dynamical Systems
publication date: 2018-04-03T00:00:00Z
review text: The author considers the perturbed Liénard system \[ \dot{x} = y\;,\;\dot{y}= - {{1}\over{4}}x(x^2-1)(x^2+2)^2 + \varepsilon (\alpha_0+\alpha_1x^2+\alpha_2x^4+\alpha_3x^6)y, \] with \(0<|\varepsilon|\ll 1\), \(\alpha_i \in \mathbb{R}\), \(i=0,1,2,3\). He considers the weak 16th Hilbert problem, thus analyzing the maximal number of zeros of the associated abelian integral. The main result reads as follows: for all \((\alpha_0,\alpha_1,\alpha_2,\alpha_3)\in \mathbb{R}^4\), the associated abelian integral has at most four zeros in the interval \((0,11/32)\).
reviewed by: Vladimir Răsvan
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 37J25
Mathematics Subject Classification ID: 34C07
zbMATH DE Number: 6855272
zbMATH Keywords: limit cycle
zbMATH Keywords: abelian integral
zbMATH Keywords: heteroclinic loop
zbMATH Keywords: hyper-elliptic Hamiltonian system
author: Xianbo Sun
MaRDI profile type: Publication
full work available at URL: s12346-015-0186-4
OpenAlex ID: W2238388259
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DOI: 10.1007/S12346-015-0186-4
description: scientific article; zbMATH DE number 6855272