{"title":"The Number of Zeros of Abelian Integral for a Quintic Hamiltonian Systems With a Rose-Figure Loop","authors":"Aiyong Chen, Huiyang Zhang","doi":"10.1080/1726037X.2020.1774157","DOIUrl":null,"url":null,"abstract":"Abstract In this article, we consider the near-Hamiltonian system where a < 0, 0 < |ε| << 1, f (x, y) and g(x, y) are polynomials of degree n ( n = 2 m , m ≥ 3, m ∈ N ). The number of isolated zeros of the corresponding Abelian integral for h ∈ is estimated.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"18 1","pages":"109 - 97"},"PeriodicalIF":0.4000,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2020.1774157","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Dynamical Systems and Geometric Theories","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/1726037X.2020.1774157","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
Abstract In this article, we consider the near-Hamiltonian system where a < 0, 0 < |ε| << 1, f (x, y) and g(x, y) are polynomials of degree n ( n = 2 m , m ≥ 3, m ∈ N ). The number of isolated zeros of the corresponding Abelian integral for h ∈ is estimated.
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