不经中心流形化简计算半单系统的最简规范形

为了在不经中心流形降维的情况下高效计算半单系统的最简规范形,基于矩阵表示法研究了半单系统的最简规范形．在系数矩阵的补算子空间上选取适当的近恒同变换代入原动力系统,求得含有低阶变换的传统规范形,通过逐次比较补算子空间上同阶项系数确定近恒同变换和系统最简规范形,利用符号运算语言Mathematica编制了计算半单系统最简规范形的通用程序,在不经过中心流形降维的情况下,可计算多种奇点类型的高维半单系统最简规范形,并给出了2个算例以证明该方法的有效性．

Computation of the Simplest Normal Form of Semi-Simple System Without Central Manifold Reduction

In order to calculate efficiently the simplest normal form(SNF)of differential semi-simple systems without center manifold reduction,the relationship between the SNF and the original equations was deducted based on matrix representation method.The near-identity transformations on complementary subspace of linear operators were substituted to original system,and the conventional normal form with low order transformations was computed.The SNF of dynamic system and the transformations were obtained by comparing the coefficients of similar terms successively.A computer program in Mathematica language was designed to perform the calcu- lation.The results show that the method can calculate SNF for many kinds of high dimension singularity systems without central manifold reduction,and two examples were given to prove the effectiveness of the program.