Finite Determinacy of High Codimension Smooth Function Germs

  • Wen-liang Gan
  • Dong-he PeiEmail author
  • Qiang Li
  • Rui-mei Gao


Mather gave the necessary and sufficient conditions for the finite 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 finitely is defined. The containment relationships of function germs still satisfy finite k-determinacy under sufficiently 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.


function germ Jacobian ideal diffeomorphism right equivalence 

MR Subject Classification

58C25 58K40 


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Copyright information

© Editorial Committee of Applied Mathematics 2019

Authors and Affiliations

  • Wen-liang Gan
    • 1
    • 2
  • Dong-he Pei
    • 1
    Email author
  • Qiang Li
    • 3
  • Rui-mei Gao
    • 4
  1. 1.School of Mathematics and StatisticsNortheast Normal UniversityChangchunChina
  2. 2.School of Mathematics and StatisticsGuizhou University of Finance and EconomicsGuiyangChina
  3. 3.School of ScienceQiqihar UniversityQiqiharChina
  4. 4.Department of ScienceChangchun University of Science and TechnologyChangchunChina

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