RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

This article is cited in 3 scientific papers (total in 3 papers)

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.

Full text: PDF file (1051 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 517.5
MSC: Primary 58A20, 58C25; Secondary 34C20
Received: 07.04.1975

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}


Linking options:
  • http://mi.mathnet.ru/eng/izv2207
  • http://mi.mathnet.ru/eng/izv/v40/i4/p855

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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  mathnet  crossref  mathscinet  zmath
    2. G. R. Belitskii, “Invariant normal forms of formal series”, Funct. Anal. Appl., 13:1 (1979), 46–47  mathnet  crossref  mathscinet  zmath
    3. Raigorodskii A.M., “Small subgraphs in preferential attachment networks”, Optim. Lett., 11:2, SI (2017), 249–257  crossref  mathscinet  isi  scopus
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:277
    Full text:87
    References:46
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021