Wuhan University Journal of Natural Sciences

, Volume 5, Issue 3, pp 257–264 | Cite as

Graded stable unfoldings in bifurcation problems

  • Zhang Guo-bin
  • Zhang Dun-mu


We introduced stability of arbitrary degree number for unfordings of bifurcation problems and established the equivalence of three stabilities. Thom's transversality theory is used to character the new stability.

Key words

Thom-transversality unfolding bifurcation 

CLC number

O 189.33 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Wassermann G.Stability of Unfoldings. Springer Lecture Notes in Mathematics 393, Berlin: Springer-Verlag, 1971.Google Scholar
  2. [2]
    Wassermann G. Stability of Unfolding in Space and Time.Acta Math, 1975,135(1):57–128.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Zou Jian-cheng. Finite Determination of Bifurcation Problems.Acta Mathematics Scientia, 1998,41(4): 818–822.Google Scholar
  4. [4]
    Zou Jian-cheng. (r,s)-Stability of Unfoldings of Bifurcation Problems.Acta Mathematica Sinica, 1998,41 (3):647–654.MathSciNetGoogle Scholar
  5. [5]
    Thom R. Un Lemme sur Applications Différentiables.Bol Soc Mexicana, 1956,2(1):59–71.MathSciNetGoogle Scholar
  6. [6]
    Thom R.Stabilité Structurelle et Morphogénése. Massachusetts: W A Benjamin, Inc, Reading, 1972.Google Scholar
  7. [7]
    Zhang Guo-bin, Yu Jian-ming. Graded Stable Unfoldings of Smooth Map-germs and Its Classifications.Advances in Mathematics, 1999,28(5):469–470.Google Scholar

Copyright information

© Springer 2000

Authors and Affiliations

  • Zhang Guo-bin
    • 1
  • Zhang Dun-mu
    • 2
  1. 1.Department of MathematicsZhanjiang Normal CollegeZhanjiangChina
  2. 2.Department of MathematicsWuhan UniversityWuhanChina

Personalised recommendations