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



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Sb. (N.S.), 1974, Volume 94(136), Number 3(7), Pages 452–467 (Mi msb3692)  

This article is cited in 2 scientific papers (total in 2 papers)

Germs of mappings $\omega$-determined with respect to a given group

G. R. Belitskii


Abstract: Let $ J(n,p)$ be the space of germs of $C^\infty$-mappings $F\colon(R^n,0)\to(R^p,0)$ and $\mathfrak G$ a group operating on $J(n,p)$. The germ $F\in J(n,p)$ is called finitely determined with respect to $\mathfrak G$ if there exists an integer $k$ such that the orbit of the germ $F$ under the action of $\mathfrak G$ is uniquely determined by the $k$-jet of the germ $F$. The germ $F$ is called $\omega$-determined with respect to the group $\mathfrak G$ if each germ $G\in J(n,p)$ that has the same formal series as $F$ at the origin lies in the orbit of $F$ under the action of $\mathfrak G$.
In this work, sufficient conditions are stated for $\omega$-determinedness. Examples are given of $\omega$-determined germs which are not finitely determined.
Bibliography: 5 titles.

Full text: PDF file (1719 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1974, 23:3, 425–440

Bibliographic databases:

UDC: 519.46
MSC: 58A20, 58C25
Received: 20.11.1973

Citation: G. R. Belitskii, “Germs of mappings $\omega$-determined with respect to a given group”, Mat. Sb. (N.S.), 94(136):3(7) (1974), 452–467; Math. USSR-Sb., 23:3 (1974), 425–440

Citation in format AMSBIB
\Bibitem{Bel74}
\by G.~R.~Belitskii
\paper Germs of mappings $\omega$-determined with respect to a~given group
\jour Mat. Sb. (N.S.)
\yr 1974
\vol 94(136)
\issue 3(7)
\pages 452--467
\mathnet{http://mi.mathnet.ru/msb3692}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=358853}
\zmath{https://zbmath.org/?q=an:0315.58002}
\transl
\jour Math. USSR-Sb.
\yr 1974
\vol 23
\issue 3
\pages 425--440
\crossref{https://doi.org/10.1070/SM1974v023n03ABEH002182}


Linking options:
  • http://mi.mathnet.ru/eng/msb3692
  • http://mi.mathnet.ru/eng/msb/v136/i3/p452

    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 for formal series and germs of $C^\infty$-mappings with respect to the action of a group”, Math. USSR-Izv., 10:4 (1976), 809–821  mathnet  crossref  mathscinet  zmath
    2. G. R. Belitskii, “Equivalence and normal forms of germs of smooth mappings”, Russian Math. Surveys, 33:1 (1978), 107–177  mathnet  crossref  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:172
    Full text:52
    References:27

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019