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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.
Received: 20.11.1973
Citation:
G. R. Belitskii, “Germs of mappings $\omega$-determined with respect to a given group”, Math. USSR-Sb., 23:3 (1974), 425–440
Linking options:
https://www.mathnet.ru/eng/sm3692https://doi.org/10.1070/SM1974v023n03ABEH002182 https://www.mathnet.ru/eng/sm/v136/i3/p452
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