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

This article is cited in 4 scientific papers (total in 4 papers)

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
Received: 13.02.1985

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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    Citing articles on Google Scholar: Russian citations, English citations
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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  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Laurent Stolovitch, “Singular complete integrability”, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, 91:1 (2000), 133  crossref  mathscinet  zmath
    3. C. O’Cadiz Gustad, “Local structure of 2 dimensional solvable Lie algebra actions on the plane”, Lobachevskii J Math, 33:4 (2012), 317  crossref
    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  mathnet  crossref  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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