Planar quasi-homogeneous polynomial systems with a given weight degree
Planar quasi-homogeneous polynomial systems with a given weight degree
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DOI：
10.3934/dcds.2016.36.4015
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发表时间：
2016-03
影响因子：
1.1
通讯作者：
Yanqin Xiong;Maoan Han
中科院分区：
文献类型：
--
作者：
Yanqin Xiong;Maoan Han
在本文中，我们研究了一类具有给定权重度的拟齐次多项式系统。首先，通过一些分析技巧，推导出此类系统的几个性质，并建立一种算法来获得给定权重程度的所有可能的显式系统。然后，我们关注此类系统的中心问题，并为中心的存在提供一些必要条件。最后，对于一个特定的拟齐次多项式系统，我们刻画了它的中心，并证明了该中心不是等时的。
In this paper, we investigate a class of quasi-homogeneous polynomial systems with a given weight degree. Firstly, by some analytical skills, several properties about this kind of systems are derived and an algorithm can be established to obtain all possible explicit systems for a given weight degree. Then, we focus on center problems for such systems and provide some necessary conditions for the existence of centers. Finally, for a specific quasi-homogeneous polynomial system, we characterize its center and prove that the center is not isochronous.