一类实平面四次微分系统的奇点量和可积性

Singular Point Quantities and Integrable properties of A Class of Real Planar Quartic Differential Systems

研究了一类只含某些2,4次项的实平面四次微分系统,根据形式级数法并利用科学计算软件Mathematica得到该系统在原点的前3个奇点量的代数递推公式,借助不变代数曲线理论讨论了系统的可积性问题.

In this paper,we study a class of real planar quartic differential systems which contains only some item 2,4 times. according to formal series method,And using scientific computing software Mathematica,The algebraic recursion formula of the first 3 singular points for this system at the origin is obtained. With the help of invariant algebraic curves theory the integrability problem for the system is discussed.