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 Z_i-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.

Key words: Z_n-equivariant singularity, resonance bifurcation, periodic parameter-excited system