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 Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 3, Pages 584–612 (Mi izv1310)

Singularities of solutions, spectral sequences, and normal forms of Lie algebras of vector fields

V. V. Lychagin

Abstract: 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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English version:
Mathematics of the USSR-Izvestiya, 1988, 30:3, 549–575

Bibliographic databases:

UDC: 514.763.85+517.9
MSC: Primary 34C20; Secondary 58C27, 58F05, 18G40, 57S20

Citation: V. V. Lychagin, “Singularities of solutions, spectral sequences, and normal forms of Lie algebras of vector fields”, Izv. Akad. Nauk SSSR Ser. Mat., 51:3 (1987), 584–612; Math. USSR-Izv., 30:3 (1988), 549–575

Citation in format AMSBIB
\Bibitem{Lyc87} \by V.~V.~Lychagin \paper Singularities of solutions, spectral sequences, and normal forms of Lie algebras of vector fields \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1987 \vol 51 \issue 3 \pages 584--612 \mathnet{http://mi.mathnet.ru/izv1310} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=903625} \zmath{https://zbmath.org/?q=an:0675.58044|0643.58039} \transl \jour Math. USSR-Izv. \yr 1988 \vol 30 \issue 3 \pages 549--575 \crossref{https://doi.org/10.1070/IM1988v030n03ABEH001030} 

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This publication is cited in the following articles:
1. O. V. Lychagina, “Normal forms of Poisson structures”, Math. Notes, 61:2 (1997), 180–192
2. Laurent Stolovitch, “Singular complete integrability”, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, 91:1 (2000), 133
3. C. O’Cadiz Gustad, “Local structure of 2 dimensional solvable Lie algebra actions on the plane”, Lobachevskii J Math, 33:4 (2012), 317
4. A. V. Akhmetzyanov, A. G. Kushner, V. V. Lychagin, “Geometric theory of special modes in the distributed-parameter control systems. I”, Autom. Remote Control, 74:11 (2013), 1786–1801
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