Geodesic
Normal forms for formal series and germs of $C^\infty$-mappings with respect to the action of a~group
Izvestiya. Mathematics , Tome 10 (1976) no. 4, pp. 809-821.

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This paper obtains a normal form for formal series and for germs of smooth mappings with respect to the action of a group. In particular, this yields a more precise version of the “resonance” normal form for differential equations. It is proved that under the action of a given group of $C^\infty$-mappings of coordinates any $C^\infty$-germ can be reduced to the sum of two germs, of which one is in normal form and the other has zero Taylor series at the origin. Bibliography: 10 titles. 
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G. R. Belitskii. Normal forms for formal series and germs of $C^\infty$-mappings with respect to the action of a~group. Izvestiya. Mathematics , Tome 10 (1976) no. 4, pp. 809-821. http://geodesic.mathdoc.fr/item/IM2_1976_10_4_a8/

[1] Sternberg S., “On the structure of local homeomorphism of Euclidean $n$-space”, Amer. J. of Mathematic, 80 (1958), 623–631 | DOI | MR | Zbl

[2] Sternberg S., “The structure of local homeomorphism”, Amer. J. of Math., 81:3 (1959), 578–604 | DOI | MR | Zbl

[3] Chen K. T., “Equivalence and decomposition of vector fields about an elementary critical points”, Amer. J. of Math., 85:4 (1965), 693–722 | DOI | MR

[4] Bryuno A. D., “Analiticheskaya forma differentsialnykh uravnenii”, Tr. Mosk. matem. obschestva, 1971, no. 25, 119–262 | Zbl

[5] Bokhner S., Martin I. T., Funktsii mnogikh kompleksnykh peremennykh, IL, M., 1951

[6] Mozer Yu., Lektsii o gamiltonovykh sistemakh, Mir, M., 1973

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

[8] Belitskii G. R., “Rostki otobrazhenii, $\omega$-opredelennye otnositelno dannoi gruppy”, Matem. sb., 94:7 (1974), 452–467

[9] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR | Zbl

[10] Belitskii G. R., “Funktsionalnye uravneniya i lokalnaya sopryazhennost otobrazhenii klassa $C^\infty$”, Matem. sb., 91:4 (1973), 565–579