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 Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 4, Pages 855–868 (Mi izv2207)

Normal forms for formal series and germs of $C^\infty$-mappings with respect to the action of a group

G. R. Belitskii

Abstract: 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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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:4, 809–821

Bibliographic databases:

UDC: 517.5
MSC: Primary 58A20, 58C25; Secondary 34C20

Citation: G. R. Belitskii, “Normal forms for formal series and germs of $C^\infty$-mappings with respect to the action of a group”, Izv. Akad. Nauk SSSR Ser. Mat., 40:4 (1976), 855–868; Math. USSR-Izv., 10:4 (1976), 809–821

Citation in format AMSBIB
\Bibitem{Bel76} \by G.~R.~Belitskii \paper Normal forms for formal series and germs of $C^\infty$-mappings with respect to the action of a~group \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1976 \vol 40 \issue 4 \pages 855--868 \mathnet{http://mi.mathnet.ru/izv2207} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=431257} \zmath{https://zbmath.org/?q=an:0363.57021} \transl \jour Math. USSR-Izv. \yr 1976 \vol 10 \issue 4 \pages 809--821 \crossref{https://doi.org/10.1070/IM1976v010n04ABEH001816} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. G. R. Belitskii, “Normal forms relative to the action of a group on a space”, Math. USSR-Izv., 11:5 (1977), 1001–1010
2. G. R. Belitskii, “Invariant normal forms of formal series”, Funct. Anal. Appl., 13:1 (1979), 46–47
3. Raigorodskii A.M., “Small subgraphs in preferential attachment networks”, Optim. Lett., 11:2, SI (2017), 249–257
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