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
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.
PDF file (1719 kB)
Mathematics of the USSR-Sbornik, 1974, 23:3, 425–440
MSC: 58A20, 58C25
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
\paper Germs of mappings $\omega$-determined with respect to a~given group
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
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
G. R. Belitskii, “Equivalence and normal forms of germs of smooth mappings”, Russian Math. Surveys, 33:1 (1978), 107–177
|Number of views:|