Geodesic
Singularities of solutions, spectral sequences, and normal forms of Lie algebras of vector fields
Izvestiya. Mathematics , Tome 30 (1988) no. 3, pp. 549-575

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A general scheme is presented for constructing solutions of systems of differential equations with a prescribed type of singularities. The scheme is then applied to the homological equation arising in the problem of classifying Lie algebras of vector fields in the neighborhood of a rest (or equilibrium) point. The formal, $C^\infty$ and $C^\omega$ variants of the classification problem are discussed. Sufficiency conditions in the contact, symplectic, and general cases are given in terms of spectral sequences. Bibliography: 18 titles. 
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     author = {V. V. Lychagin},
     title = {Singularities of solutions, spectral sequences, and normal forms of {Lie} algebras of vector fields},
     journal = {Izvestiya. Mathematics },
     pages = {549--575},
     publisher = {mathdoc},
     volume = {30},
     number = {3},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1988_30_3_a5/}
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V. V. Lychagin. Singularities of solutions, spectral sequences, and normal forms of Lie algebras of vector fields. Izvestiya. Mathematics , Tome 30 (1988) no. 3, pp. 549-575. http://geodesic.mathdoc.fr/item/IM2_1988_30_3_a5/