Z<sub>n</sub>-等变的奇点理论<sup>*</sup>

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Z_n-等变的奇点理论^*

基金项目: * 国家自然科学基金资助项目

1.
Laboratory for Nonlinear Mechanics of Continuous Media, Institute of Mechanics, Chinese Academy of Sciences, Beijng;
2.
Center of Vibration, Northwestern Polytechnic of University, Xi'an

摘要: 本文详细讨论了Z_n-等变奇点理论的基本概念,范式和万有开折的求法,并具体给出了非退化情况下Z₃-等变奇点的范式和万有开折.它们为研究周期参数激励系统的亚谐分叉提供了一种方法.
- Z_n-等变 /
- 奇点 /
- 共振分叉 /
- 参激系统
Abstract: The basic concepts, normal forms and universal unfoldings of Z_n-equivariant singularity are investigated in the present paper. As an example, the normal forms and universal unfoldings of Z₃-singularity are formulated. As a matter of fact, the theory provides a useful tool to study the subharmonic resonance bifurcation of the periodic parameter-excited system.
- Z_n-equivariant singularity /
- resonance bifurcation /
- periodic parameter-excited system /

[1]	Golubitsky M.,I.Stewart and D.G.Scheaffer,Singularities and Groups in Bifurcation Theory,Vol.1,2,Springer-Verlag,New York(1985,1988).
[2]	Sattinger.D.H.,Group Theoric Methods in Bifurcation Theory,Springer-Verlag,New York(1979).
[3]	Buzano,E.,G.Geymonant and T.Poston,Post-bucking behavior of non-linear hyperelastic thin rod with cross-section invariant under the dihedral group D.,Arch.Rational.Mech.Anal.,89,4(1985).
[4]	He Guo-wei,The Subharmonic Bifurcation of The Periodic Parameter-Excited System,Dissertation,Northwestern Polytechnical University(1991).

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