Geodesic
Normal forms relative to the action of a~group on a~space
Izvestiya. Mathematics , Tome 11 (1977) no. 5, pp. 1001-1010.

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The author proposes a normal form relative to the action of a group on a space in the presence of a filtration. Considered as examples are the actions of various groups of transformations of coordinates on the space of formal series. Bibliography: 8 titles. 
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G. R. Belitskii. Normal forms relative to the action of a~group on a~space. Izvestiya. Mathematics , Tome 11 (1977) no. 5, pp. 1001-1010. http://geodesic.mathdoc.fr/item/IM2_1977_11_5_a4/

[1] Belitskii G. R., “Normalnye formy formalnykh ryadov i rostkov $C^\infty$-otobrazhenii otnositelno deistviya gruppy”, Izv. AN SSSR. Ser. matem., 40 (1976), 855–868

[2] Mazer Dzh., “Ustoichivost $C^\infty$-otobrazhenii, III”, Matematika, 14:1 (1970), 146–175

[3] Leng S., “Hilbert's nullestellensatz in infinite-dimensional space”, Proc. Amer. Math. Soc., 3 (1952), 407–410 | DOI | MR

[4] Arnold V. I., “Normalnye formy funktsii v okrestnosti vyrozhdennykh kriticheskikh tochek”, Uspekhi matem. nauk, 29:2 (1974), 11–49 | MR

[5] Arnold V. I., “Kriticheskie tochki gladkikh funktsii i ikh normalnye formy”, Uspekhi matem. nauk, 30:5 (1975), 4–65 | MR

[6] Belitskii G. R., “O normalnykh formakh lokalnykh otobrazhenii”, Uspekhi matem. nauk, 30:1 (1975), 223 | MR

[7] Takens F., “Normal forms for certain singularities of vectorfields”, Colloque International sur l'Analyse et la Topologie Différentielle (Colloques Internationaux du Centre National de la Recherche Scientifique, Strasbourg, 1972), Ann. Inst. Fourier (Grenoble), 23:2 (1973), 163–195 | MR | Zbl

[8] Cepp Zh.-P., Algebry Li i gruppy Li, Mir, M., 1969 | MR