高次奇点的指数计算

Calculated Index Number at Higher Order Singular Point

奇点指数是刻画奇点拓扑性质的一个量 ,它是一个整数 ,本文利用 Cauchy-指标的代数工具就孤立高次奇点 ,临界奇点分别给出了一组指数计算公式 ,这是对文 [1 ]中计算公式的补充 ,尤其是对临界奇点指数计算起到了简化作用 。

The singularity index number is a quantity of topological characteristics.It is one of integer.Linear singular point index number calculation problem and higher order one inde number calculation problem where its main corresponding equations are linear have been solved successfully.In addition,using algebraic tool of Cauchy index,a set of formula is given respectively about index number calculation at critical singularity and higher order isolated singularity to the main equations.It is convenient for index number calculating,especially for the critical singularity.And index number calculation problem at singular point in analytic vector field is also solved perfectly.