Finite Determinacy of High Codimension Smooth Function Germs  

作　　者：GAN Wen-liang PEI Dong-he LI Qiang GAO Rui-mei 

机构地区：[1]School of Mathematics and Statistics, Northeast Normal University [2]School of Mathematics and Statistics, Guizhou University of Finance and Economics [3]School of Science, Qiqihar University [4]Department of Science, Changchun University of Science and Technology

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2019年第1期92-99,共8页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(11671070,11501051);NSF of Heilongjiang Province of China(QC2016008);the Project of Science and Technology of Jilin Provincial Education Department(JJKH2090547KJ)

摘　　要：Mather gave the necessary and suffcient conditions for the ?nite determinacy smooth function germs with no more than codimension 4. The theorem is very effective on determining low codimension smooth function germs. In this paper, the concept of right equivalent for smooth function germs ring generated by two ideals ?nitely is de?ned. The containment relationships of function germs still satisfy ?nite k-determinacy under suffciently small disturbance which are discussed in orbit tangent spaces. Furthermore, the methods in judging the right equivalency of Arnold function family with codimension 5 are presented.Mather gave the necessary and suffcient conditions for the ?nite determinacy smooth function germs with no more than codimension 4. The theorem is very effective on determining low codimension smooth function germs. In this paper, the concept of right equivalent for smooth function germs ring generated by two ideals ?nitely is de?ned. The containment relationships of function germs still satisfy ?nite k-determinacy under suffciently small disturbance which are discussed in orbit tangent spaces. Furthermore, the methods in judging the right equivalency of Arnold function family with codimension 5 are presented.

关 键 词：function GERM JACOBIAN ideal DIFFEOMORPHISM right EQUIVALENCE 

分 类 号：O1[理学—数学]