Applied Mathematics and Mechanics

, Volume 26, Issue 4, pp 530–538 | Cite as

Unfolding of multiparameter equivariant bifurcation problems with two groups of state variables under left-right equivalent group

Article

Abstract

Based on the left-right equivalent relation of smooth map-germs in singularity theory, the unfoldings of multiparameter equivariant bifurcation problems with respect to leftright equivalence are discussed. The state variables of such an equivariant bifurcation problem were divided into two groups, in which the first can vary independently, while the others depend on the first in the varying process. By applying related methods and techniques in the unfolding theory of smooth map-germs, the necessary and sufficient condition for an unfolding of a multiparameter equivariant bifurcation problem with two groups of state variables to be versal is obtained.

Key words

equivariant bifurcation left-right equivalent group unfolding 

Chinese Library Classification

O189.3 O177.91 

2000 Mathematics Subject Classification

58K25 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Golubitsky M, Stewart I, Schaeffer D G.Singularities and Groups in Bifurcation Theory[M]. Vol. 2, Springer-Verlag, New York, 1988, 208–246.MATHGoogle Scholar
  2. [2]
    Lari-Lavassani A, Lu Y C. Equivariant multiparameter bifurcation via singularity theory[J].J Dynamics Differential Equations, 1993,5(2): 189–218.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Futer J E, Sitta A M, Stewart I. Singularity theory and equivariant bifurcation problems with parameter symmetry[J].Math Proc Cambridge Philos Soc, 1996,120(3): 547–578.MathSciNetCrossRefGoogle Scholar
  4. [4]
    Li Yangcheng, Zou Jiancheng. Universal unfoldings of equivariant bifurcation problems with multiparameters[J].Acta Math Sinica, 1999,46(6): 1071–1076 (in Chinese).Google Scholar
  5. [5]
    Hu Fannu, Li Yangcheng. Versan unfolding of equivariant bifurcation problems with two types of state variables[J].Math Theory and Appl, 2000,20(3): 50–57 (in Chinese).MathSciNetGoogle Scholar
  6. [6]
    Li Bing, Qian Xiangzheng. The unfoldings of equivariant two-parameter bifurcation problems[J].Acta Math Sinica, 2001,44(2): 377–384 (in Chinese).MathSciNetMATHGoogle Scholar
  7. [7]
    Gao Shouping, Li Yangcheng. The unfolding of multiparameter equivariant bifurcation problem with respect to left-right equivalence[J].Annals of Math, Ser A, 2003,24(3): 341–348 (in Chinese).MATHGoogle Scholar
  8. [8]
    Li Yangcheng.Singularity Theory of Smooth Mappings[M]. Science Press, Beijing, 2002, 159–197 (in Chinese)Google Scholar
  9. [9]
    Cui Denglan, Li Yancheng. Some of finitely generated modules in equivariant singularity theory [J].J Hunan Norm Univ (Natural Science), 1996,19(4): 11–14 (in Chinese).MATHGoogle Scholar

Copyright information

© Editorial Committee of Appl. Math. Mech 2005

Authors and Affiliations

  1. 1.School of Mathematics and Computing TechnologyCentral South UniversityChangshaP. R. China
  2. 2.College of Mathematics and Computer ScienceHunan Normal UniversityChangshaP. R. China

Personalised recommendations