中文摘要：

如果自治系统接受一个单参数Lie群,那么可以构造性地得到该系统的首次积分.基于不变流形寻找自治系统所接受的单参数Lie群,进而得到该系统的首次积分.

英文摘要：

If a particular single-parameter Lie group is admitted by an autonomous system,then the first integrals of the system can be obtained by constructing method.In this paper,a particular single-parameter Lie group,which is admitted by autonomous system,can be found by invariant manifold principle.Hence,the first integral of the system can be obtained.