Abelian integrals for cubic vector fields
type: Item
instance of: scholarly article
title: Abelian integrals for cubic vector fields
zbMATH Open document ID: 0958.34026
DOI: 10.1007/BF02505998
author: Yulin Zhao
author: Zhifen Zhang
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2001-04-09T00:00:00Z
review text: The authors prove that the lowest upper bound of the number of the isolated zeros to the Abelian integral \[ I(h)= \oint_{\Gamma_h}(\alpha+ \beta x+\gamma x^2)y dx \] is two for \(h\in (-1/12,0)\), where \(\Gamma_h\) is the compact component of \(H(x, y)= (1/2)y^2+ (1/3) x^3+ (1/4)x^4= h,\alpha, \beta,\gamma\) are arbitrary constants.
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C08
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C37
zbMATH DE Number: 1472040
zbMATH Keywords: perturbed system
zbMATH Keywords: bifurcation
zbMATH Keywords: number of limit cycles
reviewed by: Lansun Chen
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02505998
OpenAlex ID: W1980979667
description: scientific article; zbMATH DE number 1472040