Planar quasi-homogeneous polynomial differential systems and their integrability
Planar quasi-homogeneous polynomial differential systems and their integrability
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DOI：
10.1016/j.jde.2013.07.032
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发表时间：
2013-11
影响因子：
2.4
通讯作者：
Belen García;J. Llibre;Jesús S. Pérez del Río
中科院分区：
文献类型：
--
作者：
Belen García;J. Llibre;Jesús S. Pérez del Río
本文研究了拟齐次多项式微分系统，给出了一个求给定次数的拟齐次多项式微分系统的算法。利用该算法，我们得到了所有的2次和3次拟齐次向量场。拟齐次多项式微分系统是Liouville可积的。特别是，我们刻画了所有的拟齐次向量场的次数2和3有一个多项式，合理的或整体的解析第一积分。
In this paper we study the quasi-homogeneous polynomial differential systems and provide an algorithm for obtaining all these systems with a given degree. Using this algorithm we obtain all quasi-homogeneous vector fields of degree 2 and 3.The quasi-homogeneous polynomial differential systems are Liouvillian integrable. In particular, we characterize all the quasi-homogeneous vector fields of degree 2 and 3 having a polynomial, rational or global analytical first integral.