Versal unfolding of homogeneous cubic degenerate centers in strong monodromic family
Versal unfolding of homogeneous cubic degenerate centers in strong monodromic family
复制标题
强单向族中齐次立方简并中心的全展开
DOI：
10.1016/j.jde.2021.02.038
复制
发表时间：
2021
影响因子：
2.4
通讯作者：
Zhang Weinian
中科院分区：
文献类型：
--
作者：
Liu Lingling;Tang Yilei;Zhang Weinian
本文在强单值族中全面展开了一个不适用Poincaré标准形的齐次三次退化中心。化为强单值类的规范型，证明了带扰动的齐次三次退化中心的退化是余维1的。利用一个开折参数，我们证明了强单值族的中心分支，这表明当三阶广义李雅普诺夫量不为零时，至多出现一个极限环.
In this paper we versally unfold a homogeneous cubic degenerate center, to which the Poincaré normal form is not applicable, in the strong monodromic family. Reducing to a normal form of the strong monodromic class, we prove that the degeneracy of the homogeneous cubic degenerate center with perturbations is of codimension one. Using one unfolding parameter, we display bifurcations at the center in the strong monodromic family, which shows that at most one limit cycle arises if the 3-th order generalized Lyapunov quantity does not vanish.