一类Poincaré系统的中心条件及极限环个数

Center Condition and Limit Cycles for A Class of Poincaré Systems

考虑了形如x=-y+x(a+f1(x,y)+fn(x,y)),y=x+y(a+f1(x,y)+fn(x,y))的Poincaré系统,这里fn(x,y)是n次齐次多项式,得到了当n=4,5,…,8时系统的中心条件及细焦点的阶数和极限环个数。

This paper consider the following forms of Poincaré system x^·=-y＋x（a＋f1（x,y）＋fn（x,y））y^·=x＋y（a＋f1（x,y）＋fn（x,y））where fn （x, y） is real homogeneous polynomial of degree n. In the cases where n=4,5,…,8, we get the center condition and limit cycles number of the system.