解析系统初等奇点逆积分因子的存在性

Existence of Inverse Integrating Factors at Elementary Singular Point

由于逆积分因子的存在性与平面解析系统的可积性之间存在密切联系,因此它是研究平面解析系统可积性的重要工具。对于含初等奇点的平面解析系统,证明了它相应的正规形系统总存在逆积分因子,并求出其逆积分因子的具体表达式;利用坐标变换下两个平面系统逆积分因子之间的关系,证明了在初等奇点总存在逆积分因子。

Since there exists closely relat ionship between the existence of lnverse lntegrating factors and the integrability of analytic planar system,it is an important tool to study the ntegrability problem of analytic planar system. For an analytic planar system with an elementary singular point, th e e x is te n c e o f the inverse ntegrating factor for its associated normal form is proved , an d th e e x p re s s io n o f th e in v e rs eintegrating factor is given. Then by using the relationship between inverse integrating factors of theoriginal system and the transformed system by a coordinate transformation,the result that there is an inverse integrating factors at an elementary singular point is proved.