GUO Rui-zhi, LI Yang-cheng. Unfolding of Multiparameter Equivariant Bifurcation Problems With Two Groups of State Variables Under Left-Right Equivalent Group[J]. Applied Mathematics and Mechanics, 2005, 26(4): 489-496.
 Citation: GUO Rui-zhi, LI Yang-cheng. Unfolding of Multiparameter Equivariant Bifurcation Problems With Two Groups of State Variables Under Left-Right Equivalent Group[J]. Applied Mathematics and Mechanics, 2005, 26(4): 489-496.

# Unfolding of Multiparameter Equivariant Bifurcation Problems With Two Groups of State Variables Under Left-Right Equivalent Group

• Received Date: 2003-08-18
• Rev Recd Date: 2004-12-06
• Publish Date: 2005-04-15
• Based on the left-right equivalent relation of smooth map-germs in singularity theory,the unfoldings of multiparameter equivariant bifurcation problems with respect to left-right 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.
•  [1] Golubitsky M, Stewart I,Schaeffer D G.Singularities and Groups in Bifurcation Theory[M].Vol.2. New York:Springer-Verlag, 1988，208—246. [2] Lari-Lavassani A, Lu Y C.Equivariant multiparameter bifurcation via singularity theory[J].J Dynamics Differential Equations，1993,5(2):189—218. [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. [4] 李养成，邹建成.带有多个分歧参数的等变分歧问题的万有开折[J].数学学报，1999，46(6)：1071—1076. [5] 胡凡努，李养成.关于两状态变量组的等变分歧问题的通用开折[J].数学理论与应用，2000，20(3)：50—57. [6] 李兵，钱祥征.等变两参数分歧问题的开折[J].数学学报，2001，44(2)：377—384. [7] 高守平，李养成.多参数等变分歧问题关于左右等价的开折[J].数学年刊，A辑，2003，24(3)：341—348. [8] 李养成.光滑映射的奇点理论[M].北京：科学出版社，2002,159—197. [9] 崔登兰，李养成.等变奇点理论中的一类有限生成模[J].湖南师范大学自然科学学报，1996，19(4)：11—14.

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