Germs of mappings $\omega$-determined with respect to a given group
Sbornik. Mathematics, Tome 23 (1974) no. 3, pp. 425-440
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.
@article{SM_1974_23_3_a6,
author = {G. R. Belitskii},
title = {Germs of mappings $\omega$-determined with respect to a~given group},
journal = {Sbornik. Mathematics},
pages = {425--440},
year = {1974},
volume = {23},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1974_23_3_a6/}
}
G. R. Belitskii. Germs of mappings $\omega$-determined with respect to a given group. Sbornik. Mathematics, Tome 23 (1974) no. 3, pp. 425-440. http://geodesic.mathdoc.fr/item/SM_1974_23_3_a6/
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