Classification Of Two-dimensional Subanalytic Sets Under Bi-Lipschitz Equivalence Relation

The singularity theory is a new branch of modern mathematics,it is a subject of numerous mathematical discipline intersection,the focus is the study of the problem such as mapping,bud,classification,and the development of The Times analytic set can date back to the 1950 s,by the H.C Artan,H.W.Hitney,F.B Ruhat people such as research,put forward the real analytical set,the definition of semi-analytical set resol-tion and time set.Lipschitz geometric mapping is a rapidly developing discipline in contemporary singularity theory,and the results of this research are the"tameness"theorem proved by some researchers,while the bi-Lipschitz classification of functional buds only em-erged in 2003^[1,2].Although both the sub-analytic set and bi-Lipschitz mapping have rich knowled-ge bases in their respective fields,there are few theories that can combine them toget-her.Based on the existing theories of the sub-analytic set and bi-Lipschitz mapping,this paper studies the classification of the sub-analytic set under the bi-Lipschitz equi-valence relation by combining the theories of the sub-analytic set and bi-Lipschitz m-apping.This paper focuses on the classification of sub-analytic sets,which consists of three chapters.The first chapter introduces the basic knowledge needed in this paper,proposes the definitions and basic properties of sub-analytic set and bi-Lipschitz,as well as the definitions of combinatorial equivalence and H(?)lder triangle.In the second chapter some preliminary theorems are proposed,such as structure theorem,Horn theorem and reduction theorem,etc.These theorems are the precondit-ions for the proof of classification theorem in the third chapter.In the third chapter,the classification of subanalytic sets under the bi-Lipschitz equivalence relation and a corollary are proposed:under what conditions are the buds of two subanalytic sets equivalent to bi-Lipschitz?...