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 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.

Key words: left-right equivalent group, unfolding, equivariant bifurcation