具有幂零奇点三维系统的二次规范型及普适开折

Quadratic Normal Forms and Universal Unfoldings of Three-Dimensional Systems with Nilpotent Singular Points

摘要: 本文对三维动力系统中三类具有幂零奇点的微分方程进行了讨论和分析，通过规范型理论得出了含有二次多项式的规范型，再利用坐标平移得出了它们的普适开折。

Abstract: In this paper, for three-dimensional dynamic systems, we discuss and analyze three classes of eq-uations which have nilpotent singular points. The normal forms of quadratic polynomials are ob-tained by normal formal theory. Then, the universal unfoldings are obtained by using coordinate translation.