Classification of $\mathbb{Z}_3$-Equivariant Simple Function Germs

The present paper deals with the classification of multivariate holomorphic function germs that are equivariant simple under representations of cyclic groups. We obtain a complete classification of such function germs of two and three variables for all possible nontrivial $\mathbb{Z}_3$-actions. Our main classification methods generalize those used for the classification of simple germs in the nonequivariant case.