摘要
考虑一类具有全局中心的(m,1)型拟齐次多项式平面微分系统,通过探讨阿贝尔积分的零点个数,分别研究该系统在n次多项式和在(n,1)型拟齐次多项式扰动下,从中心的周期环域分支出来的极限环个数,给出了这些个数的上界并证明它们是可达的.
This paper considers a class of(m,1)-quasi-homogeneous polynomial planar differential systems with global center.By studying the number of zeros of Abelian integrals,we obtain the number of limit cycles bifurcating from the period annulus of the center of the system,separately under the perturbation of polynomial of degree n,and the(n,1)-quasihomogeneous polynomial.Moreover,the upper bound of these numbers are given and are proved to be reachable.
作者
何泽涔
梁海华
HE Ze-cen;LIANG Hai-hua(School of Mathematics and Systems Science,Guangdong Polytechnic Normal University,Guangzhou 510665,China)
出处
《数学的实践与认识》
北大核心
2019年第9期311-320,共10页
Mathematics in Practice and Theory
基金
国家自然科学基金(11771101)
广东省普通高校重大科研项目(2017KZDXM054)
广东省科技计划项目(20168090927009)
关键词
拟齐次
多项式系统
中心
极限环
阿贝尔积分
quasi-homogeneous
polynomial system
center
limit cycles
Abelian integral
