一类三次系统两个中心共存的条件  

Conditions for certain cubic systems to have two centers

作　　者：梁肇军[1] 

机构地区：[1]华中师范大学数学与统计学学院,武汉430079

出　　处：《华中师范大学学报（自然科学版）》2003年第4期445-450,共6页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金资助项目(19871033).

摘　　要：对于一类平面三次系统dxdt=y+a1x2+(a2+2b1)xy+(a3-a1)y2+xf(x,y),dydt=-x+b1x2+(b2-2a1)xy-b1y2+yf(x,y),(1)其中f(x,y)≡a4x2+a5xy+(a6-a4)y2.N.G.Lloyd,C.J.Christopher等研究了系统(1)的原点是中心的充要条件.除原点O(0,0)之外,如果系统(1)还存在另一奇点,它是中心或焦点型的(即在奇点处一次近似系统为中心),本文讨论系统(1)的两个中心共存的条件.In this paper, the quadratic-like cubic systems dxdt=y+a_1x^2+(a_2+2b_1)xy+(a_3-a_1)y^2+xf(x,y),dydt=-x+b_1x^2+(b_2-2a_1)xy-b_1y^2+yf(x,y), (1)in which f(x,y)=a_4x^2+a_5xy+(a_6-a_4)y^2 is considered. N.G.Lloyd and C.J.Christopher et al.studied the sufficient conditions for that, the origin of the system(1) is a center. Our interest is the coexistence of two centers for the system(1). The conditions for the system(1) to have two centers is also briefly given.

关 键 词：非线性微分方程 三次系统 双中心 

分 类 号：O151.12[理学—数学]