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

在由Se-Ashi原理得到的有限类型微分方程组中，我们确定了一类具有非常丰富的无穷小对称性的有限类型微分方程组。此外，我们还显式地写出了这类有限类型方程的模型方程。此外，我们还研究了二阶接触几何领域中的基本归约过程，建立了两个基本归约定理。

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.