Unfoldings of Equivariant Bifurcation Problems with Parameter Symmetry under a Left-Right Equivalent Group

Based on the theory of left-right equivalence of smooth map germs in sigularity theory,multiparameter equivariant bifurcation problems of state varibles with symmetry and parameters with symmetry were introduced.The unfoldings of such equivariant bifurcation problems with respect to left-right equivalence were discussed.The necessary and sufficient conditions for an unfolding of such a multiparameter equivariant bifurcation problem to be versal were obtained.