Geodesic
Normal forms for formal series and germs of $C^\infty$-mappings with respect to the action of a~group
Izvestiya. Mathematics , Tome 10 (1976) no. 4, pp. 809-821

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This paper obtains a normal form for formal series and for germs of smooth mappings with respect to the action of a group. In particular, this yields a more precise version of the “resonance” normal form for differential equations. It is proved that under the action of a given group of $C^\infty$-mappings of coordinates any $C^\infty$-germ can be reduced to the sum of two germs, of which one is in normal form and the other has zero Taylor series at the origin. Bibliography: 10 titles. 
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     author = {G. R. Belitskii},
     title = {Normal forms for formal series and germs of $C^\infty$-mappings with respect to the action of a~group},
     journal = {Izvestiya. Mathematics },
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1976_10_4_a8/}
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G. R. Belitskii. Normal forms for formal series and germs of $C^\infty$-mappings with respect to the action of a~group. Izvestiya. Mathematics , Tome 10 (1976) no. 4, pp. 809-821. http://geodesic.mathdoc.fr/item/IM2_1976_10_4_a8/