一类扰动七次哈密顿系统的极限环  

Limit Cycles for a Class of Perturbed Seventh Order Hamiltonian Systems

作　　者：张景涛 余秋里 洪晓春[1] ZHANG Jingtao;YU Qiuli;HONG Xiaochun(School of Statistics and Mathematics,Yunnan University of Finance and Economics,Kunming Yunnan 650221,China)

机构地区：[1]云南财经大学统计与数学学院,云南昆明650221

出　　处：《曲靖师范学院学报》2022年第3期8-11,15,共5页Journal of Qujing Normal University

基　　金：国家自然科学基金项目“几类平面微分系统的极限环数目上下界及分布情况”(11761075).

摘　　要：研究了一类带有幂零奇点的七次超椭圆哈密顿系统在特殊七次多项式扰动下的极限环情况.应用判定函数和数值模拟方法得出该系统在无界环域中有3个极限环,而且模拟出了这些极限环的具体位置.The limit cycles of a class of seventh order hyperelliptic Hamiltonian systems with nilpotent singular points under the perturbation of seventh degree polynomial are studied to find that the system has three limit cycles in the unbounded ring domain,and the specific positions of these limit cycles are simulated by using the detection function and numerical simulation method.

关 键 词：极限环 哈密顿系统 阿贝尔积分 判定函数 

分 类 号：O175.12[理学—数学]