一类Z2-等变扰动的三次哈密顿系统极限环的个数与分布

数学季刊 ›› 2011, Vol. 26 ›› Issue (1): 144-151.

一类Z₂-等变扰动的三次哈密顿系统极限环的个数与分布

School of Mathematical Sciences, Xuchang University

收稿日期:2007-04-16 出版日期:2011-03-30 发布日期:2023-05-15
作者简介:ZHOU Hong-xian(1978- ), male, native of Nanyang, Henan, a lecturer of Xuchang University, Ph.D., engages in diﬀerential equations and dynamical systems.
基金资助:
Supported by the Natural Science Foundation of China(10802043,10826092)；

The Number and Distributions of Limit Cycles of a Cubic Hamiltonian System with Z₂-symmetry Perturbation

School of Mathematical Sciences, Xuchang University

Received:2007-04-16 Online:2011-03-30 Published:2023-05-15
About author:ZHOU Hong-xian(1978- ), male, native of Nanyang, Henan, a lecturer of Xuchang University, Ph.D., engages in diﬀerential equations and dynamical systems.
Supported by:
Supported by the Natural Science Foundation of China(10802043,10826092)；

摘要/Abstract

摘要： This paper is concerned with the number and distributions of limit cycles of a cubic Z₂-symmetry Hamiltonian system under quintic perturbation. By using qualitative analysis of differential equation, bifurcation theory of dynamical systems and the method of detection function, we obtain that this system exists at least 14 limit cycles with the distribution C¹_9...C₁²)].

关键词: limit cycles, bifurcation, detection functions, Hamiltonian system

Abstract: This paper is concerned with the number and distributions of limit cycles of a cubic Z₂-symmetry Hamiltonian system under quintic perturbation. By using qualitative analysis of differential equation, bifurcation theory of dynamical systems and the method of detection function, we obtain that this system exists at least 14 limit cycles with the distribution C¹_9...C₁²)].

Key words: limit cycles, bifurcation, detection functions, Hamiltonian system

中图分类号:

O175

周宏宪, 张燕. 一类Z₂-等变扰动的三次哈密顿系统极限环的个数与分布[J]. 数学季刊, 2011, 26(1): 144-151.

ZHOU Hong-xian, ZHANG Yan. The Number and Distributions of Limit Cycles of a Cubic Hamiltonian System with Z₂-symmetry Perturbation[J]. Chinese Quarterly Journal of Mathematics, 2011, 26(1): 144-151.

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一类Z₂-等变扰动的三次哈密顿系统极限环的个数与分布

The Number and Distributions of Limit Cycles of a Cubic Hamiltonian System with Z₂-symmetry Perturbation

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