versal

Strong Relative A_ ( S , T ) Finite Determinacy of Map Germs and Relation with Relative Versal Unfolding

相对映射芽的强有限决定性与通用开折

In this paper , we make use of relative transverality unfolding to study the relation of strong relative AS , T finite determinacy of map germs with relative versal unfolding .

用奇点理论中横截开折的理论对相对映射芽的强有限决定性与通用开折之间的关系进行了研究。

Versal Deformations of Relative Smooth Map-germs with Respect to Contact Equivalence

接触等价下的相对映射芽的通用形变

A Note on the versal - unfolding of equivariant bifurcation problems

关于等变分歧问题的通用开折的注记

We prove the strong relative AS , T finite determinacy of map germs and the relative versal unfolding are equivalent .

证明了相对映射芽的强有限决定性与相对映射芽的通用开折存在性之间的等价关系，即相对映射芽f是强有限决定的当且仅当f具有通用开折。

These changes are called bifurcations . If bifurcations or even a versal unfolding are given , all physical phenomena of this system are clear .

弄清了系统的分岔甚至给出了它的普适开折，该系统所发生的所有物理现象都将昭然若示。

The Invariance of Versal Unfoldings Under Γ - Equivalence

开折的Γ-等价不变性

The values of Kdmax / Kd are 20.49 , 16.86 , 20.60 , 5.30 , respectively ; and form in versal ratio to foc of soil .

Kdmax/Kd比值则分别为20.49,16.86,20.60,5.30，与土壤的foc成反比。

Therefore , in order to exhibit all phenomena in its Bogdanov-Takens bifurcation ( in particular , those phenomena not displayed before ), we reduce the original system to its normal form and give a versal unfolding to the parameters κ,ρ .

所以，为了展示系统Bogdanov-Takens分岔中的所有现象（特别是，在已有文献中没有涉及到的现象），我们化系统为它的正规形并且给出关于参数κ，ρ的普适开折。