Research on the differential sysytems and geometric structures associated with simple graded Lie algebras

在由Se-ashi原理得到的有限型微分方程中，我们确定了一类具有极其丰富的无穷小对称性的有限型微分方程。并明确地给出了这类有限型方程的模型方程。进一步研究了二阶接触几何中的基本约简过程，给出了两个基本约简定理。

We determined the class of differential equations of finite type, which admits extraordinarily rich infinitesimal symmetries, among the classes of differential equations of finite type obtained from the Se-ashi's principle. Moreover we write up explicitly the model equations of this class of finite type equations. Furthermore we investigated the fundamental Reduction procedure in the fields of Contact Geometry of second Order and formulated two fundamental Reduction Theorems.