Planar real polynomial differential systems of degree $n> 3$ having a weak focus of high order
Planar real polynomial differential systems of degree $n> 3$ having a weak focus of high order
复制标题
DOI：
10.1216/rmj-2012-42-2-657
复制
发表时间：
2012-04
影响因子：
0.8
通讯作者：
J. Llibre;Roland Rabanal
中科院分区：
文献类型：
--
作者：
J. Llibre;Roland Rabanal
我们构造了偶数（分别为奇数）次n > 3的平面多项式微分系统，其形式为线性加上一个n次的非线性齐次部分，在原点有一个n2 − 1（分别为n2−1/2）阶的弱焦点。据我们所知，这提供了迄今为止已知的任意次数n的多项式微分系统的弱焦点的最高阶。
We construct planar polynomial differential systems of even (respectively odd) degree n > 3, of the form linear plus a nonlinear homogeneous part of degree n having a weak focus of order n2 − 1 (respectively n2−1/2) at the origin. As far as we know this provides the highest order known until now for a weak focus of a polynomial differential system of arbitrary degree n.