MONOTONICITY OF THE RATIOS OF TWO ABELIAN INTEGRALS FOR HAMILTONIAN SYSTEMS WITH PARAMETERS

被引：0

作者：

Wang, Qiaoyun ^{[1
]}

Wang, Na ^{[2
]}

Sun, Xianbo ^{[3
]}

机构：

[1] Guangxi Univ, Dept Math, Nanning 530004, Guangxi, Peoples R China

[2] Beijing Informat Sci & Technol, Sch Appl Sceince, Beijing 100192, Peoples R China

[3] Hangzhou Normal Univ, Sch Math, Hangzhou 311121, Zhejiang, Peoples R China

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2024年 / 14卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Abelian integral; monotonicity; Hamiltonian system; HYPERELLIPTIC INTEGRALS; DEGREE-4; PERTURBATIONS; CRITERION; WAVES; ZEROS;

D O I：

10.11948/20220349

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the monotonicity of the ratios of two Abelian integrals closed integral(gamma i(h)) ydx \ closed integral(gamma i)(h) xydx over three period annuli {gamma(i)(h)}, for i = 1, 2, 3, defined by a seventh-degree hyperelliptic Hamiltonian H(x, y) = y(2) + Psi(x) with a parameter. The parameter makes the problem more challenging to analyze. To overcome the difficulty, we apply some criterion with the help of transformations, tools in computer algebra such as boundary polynomial theory to determine the monotonicity of the ratios. Our results establish the existence and uniqueness of limit cycle bifurcated from each period annulus.

引用

页码：2466 / 2487

页数：22

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