本文研究动力系统的线性群作用,该群的李代数与系统的向量场作用, 以及两者间的关系. 并将其结果应用于$n$阶旋转群, 给出了$n$阶旋转对称非线性系统的一般结构表达式.

The paper investigates the action of the linear group on dynamic systems, the interaction of its Lie algebra with the vector fields of the systems and the relationship between them. The results are applied to the $n$-th order orthogonal group. The general structure of the $n$-th order nonlinear systems with rotatable symmetry is given.