常微分方程组接受单参数李群的判定条件

Criterion Conditions of Ordinary Differential Equation System Accepting One-Parameter Lie Group

通过引入常微分方程组变量的无穷小变换,给出自治与非自治常微分方程组接受单参数李群的判定条件,从而推广了管克英等关于自治常微分方程组接受单参数李群的充要条件.

Some criterion conditions of system of automatic and nonautomatic ordinary differential equations accepting one-parameter Lie group are established by using infinitesimal transforms of the variables of the system. Thereby, the sufficient and necessary condition on an automatic ordinary differential equations system accepting one-parameter Lie group, that is given by Guan Ke-ying, et al, is extended.