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

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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.

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Authors and Affiliations

  1. School of Mathematics and Computing Technology, Central South University, 410083, Changsha, P. R. China

    Guo Rui-zhi (Associate Professor, Doctor) & Li Yang-cheng

  2. College of Mathematics and Computer Science, Hunan Normal University, 410081, Changsha, P. R. China

    Guo Rui-zhi (Associate Professor, Doctor)

Authors
  1. Guo Rui-zhi
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  2. Li Yang-cheng
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Corresponding author

Correspondence to Guo Rui-zhi.

Additional information

Communicated by Guo Xing-ming

Project supported by the National Natural Science Foundation of China (No. 10271023); the Natural Science Foundation of Human Province of China (No. 04JJ3072) and the Science Foundation of Human Province Government of Education (No. 04C383)

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Rui-zhi, G., Yang-cheng, L. Unfolding of multiparameter equivariant bifurcation problems with two groups of state variables under left-right equivalent group. Appl Math Mech 26, 530–538 (2005). https://doi.org/10.1007/BF02465393

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  • DOI: https://doi.org/10.1007/BF02465393

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2000 Mathematics Subject Classification

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