Perturbation of a Period Annulus Bounded by a Saddle-Saddle Cycle in a Hyperelliptic Hamiltonian Systems of Degree Seven

被引：1

作者：

Yang, Sumin ^{[1
,2
]}

Qin, Bin ^{[1
]}

Xia, Guoen ^{[1
]}

Xia, Yong-Hui ^{[3
]}

机构：

[1] Guangxi Univ Finance & Econ, Dept Appl Math, Nanning 530003, Guangxi, Peoples R China

[2] Guangxi Technol Coll Machinery & Elect, Dept Human Sci, Nanning 530007, Guangxi, Peoples R China

[3] Zhejiang Normal Univ, Sch Math Sci, Jinhua 321000, Zhejiang, Peoples R China

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2020年 / 19卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Limit cycles; Heteroclinic loop; Nilpotent cusp; Abelian integral; Poincare bifurcation; Weak Hilbert's 16th problem; LIMIT-CYCLES; DIFFERENTIAL-SYSTEMS; BIFURCATION; NUMBER; LOOP;

D O I：

10.1007/s12346-020-00348-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the limit cycle bifurcation by perturbing the period annuluses of two perturbed hyper-elliptic Hamiltonian systems of degree seven. The period annuluses are bounded by heteroclinic loops, inside or outside of which there exist two nilpotent cusps. The bifurcation function is Abelian integral which is the first-order approximation of the Poincare map. The sharp bounds of the number of limit cycles bifurcated from the periodic annuluses are obtained by Chebyshev criterion and asymptotic analysis.

引用

页数：20

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