The Research On The Relationship Between Equivariant Gradient Bifurcation Problems And Invariant Potential Function Germs

In this paper,the mapping germs are introduced into symmetry and contact equivalence group,the concepts of equivariant bifurcation,gradient mapping germs and potential function germs are given,the corresponding tangent spaces under various equivalent groups are calculated,the relationship between equivariant gradient bifurcation problems and invariant potential function germs is studied by using singularity theory and group theory,and the relevant conclusions are obtained.This paper consists of four chapters.In the first chapter: we introduce the background knowledge related to the content of the paper and the current research situation,expound the problems and significance of the paper.In the second chapter: we mainly introduce the definition and conclusion related to the content of the paper.In the third chapter: we introduce the relevant knowledge of equivariant gradient bifurcation problems.In the fourth chapter: we give the main conclusions,proofs,and demonstrate the relationship between the equivariant gradient bifurcation problems and the invariant potential function germs.