The Versal Deformation And Transversality Of Multigerms

This paper mainly studies the problem between the versal deformation and transversality of multi-function germs.Singularity theory is a new branch of modern mathematics,and it is widely used in physics,chemistry,biology and some engineering fields.The 1930 s was the embryonic period of the singularity.H.M.Morse's critical point theory was the earliest research on the singularity theory.In 1955,the American mathematician H.Whitney published the paper of mapping of the plane to the plane.Since then,the singularity theory of smooth mapping has flourished,and it has become one of the most important research in the field of mathematics.The development of singularity theory has gradually enriched its content,and discussing the deformation of different types of germs is one of the hot research topics in singularity theory.Regarding the deformation theory,it is mainly to explore the changes of the germs before and after the disturbance.That is,if a germ has versal deformation,then every deformation produced after a certain disturbance to the germ can be derived from its versal deformation.This article uses the singularity theory as a tool to expand the research on the deformation of single function germ to the research and discussion of the deformation theory of multigerms.The structure of this article is as follows: Chapter 1 is the Introduction,we first introduce the development process of singularity theory,and summarizes the research status and results of multigerms theory in singularity theory;Chapter 2 is the Preliminaries,we describe some basic concepts and symbol definitions about multigerms;In Chapter 3,we make preparations for the proof of the versal deformation theorem for multi-function germs;In Chapter 4,we give the versal deformation theorem of multi-function germs and its corollaries,and the relationship between the versal deformation and transversality of multi germs is explained.