Universal Unfolding And Finite Determinacy Of Equivariant Mapping Germs Under Contaction Equivalence Group

In this paper,we introduces symmetry and contaction equivalence group for the mapping germs,discusses the universal unfolding and finite determinacy of the equiv-ariant mapping germs under the contaction equivalence group.And we get some corre-sponding results.This paper consists of four chapters.In the first chapter:We have introduce dynamic state,the backgroundsand,and the important work of this paper.In the second chapter:We introduce some basic concepts and main conclusion.In the third chapter:We study the algebraic lemma and geometric lemma of equiv-ariant mapping germs,and obtained that the unfolding of equivariant mapping germs is a necessary and sufficient condition for universal unfolding.In the fourth chapter:We mainly give that the equivariant mapping germ is a suffi-cient condition for the finite determinacy and a necessary condition for the finite deter-minacy.