Geodesic
Classification of $\mathbb{Z}_3$-Equivariant Simple Function Germs
Matematičeskie zametki, Tome 105 (2019) no. 2, pp. 163-178

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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.
Keywords: $G$-space, classification of singularities, equivariant mapping, simple germ. 
@article{MZM_2019_105_2_a0,
     author = {E. A. Astashov},
     title = {Classification of $\mathbb{Z}_3${-Equivariant} {Simple} {Function} {Germs}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {163--178},
     publisher = {mathdoc},
     volume = {105},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_2_a0/}
}
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E. A. Astashov. Classification of $\mathbb{Z}_3$-Equivariant Simple Function Germs. Matematičeskie zametki, Tome 105 (2019) no. 2, pp. 163-178. http://geodesic.mathdoc.fr/item/MZM_2019_105_2_a0/