【摘要】 讨论一类四次多项式微分系统的中心条件与极限环分支问题。通过对该实系统所对应的伴随复系统奇点量的计算,得到系统的原点成为中心的必要条件,并对它的充分性进行严格的证明。从奇点量导出焦点量,得到了原点成为8阶细焦点的条件,最后证明该系统从在原点邻域有8个小振幅极限环。这是首次得到四次系统在细焦点可分支出8个极限环。更多还原

【Abstract】 The bifurcation of limit cycles and conditions of origin to be a center for a biquadratic polynomial system is investigated.By the computation of the singular point values for the concomitant complex system of the real system,the necessary conditions of origin of system to be a center is obtained,and the sufficiency for the conditions is strictly proven.The focal values are derived from of the singular points,and the conditions that the origin to be an 8 order weak focal is obtained.Finally,it is proved that this system has small amplitude limit cycles in the neighborhood of the origin.This is the first time that an example of a biquadratic system with eight limit cycles bifurcated from a weak focal is given.更多还原