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

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.

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

Bibliographic databases:

UDC: 519.46
MSC: 58A20, 58C25

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} 

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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
2. G. R. Belitskii, “Equivalence and normal forms of germs of smooth mappings”, Russian Math. Surveys, 33:1 (1978), 107–177
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