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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IM2_1988_30_3_a5,
     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/}
}
TY  - JOUR
AU  - V. V. Lychagin
TI  - Singularities of solutions, spectral sequences, and normal forms of Lie algebras of vector fields
JO  - Izvestiya. Mathematics 
PY  - 1988
SP  - 549
EP  - 575
VL  - 30
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1988_30_3_a5/
LA  - en
ID  - IM2_1988_30_3_a5
ER  - 
%0 Journal Article
%A V. V. Lychagin
%T Singularities of solutions, spectral sequences, and normal forms of Lie algebras of vector fields
%J Izvestiya. Mathematics 
%D 1988
%P 549-575
%V 30
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1988_30_3_a5/
%G en
%F IM2_1988_30_3_a5
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/

[1] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M, 1974 | MR

[2] Arnold V. I., “Spektralnye posledovatelnosti dlya privedeniya funktsii k normalnym formam”, Zadachi mekhaniki i matematicheskoi fiziki, Nauka, M., 1976, 7–20

[3] Godeman R., Algebraicheskaya topologiya i teoriya puchkov, IL, M., 1961

[4] Kushnirenko A. G., “Analiticheskoe deistvie poluprostoi gruppy Li v okrestnosti nepodvizhnoi tochki ekvivalentno lineinomu”, Funkts. analiz., 1:1 (1967), 103–104 | Zbl

[5] Likhnerovich A., Teoriya svyaznostei v tselom i gruppy golonomii, IL, M., 1960

[6] Lychagin V. V., “Lokalnaya klassifikatsiya nelineinykh differentsialnykh uravnenii v chastnykh proizvodnykh pervogo poryadka”, Uspekhi matem. nauk, 30:1 (1975), 101–171 | MR | Zbl

[7] Lychagin V. V., “Dostatochnye orbity gruppy kontaktnykh diffeomorfizmov”, Matem. sb., 104:2 (1977), 248–270 | MR | Zbl

[8] Lychagin V. V., “Ob osobennostyakh reshenii differentsialnykh uravnenii”, Dokl. AN SSSR, 251:4 (1980), 794–799 | MR | Zbl

[9] Lychagin V. V., “Spektralnye posledovatelnosti i normalnye formy algebr Li vektornykh polei”, Uspekhi matem. nauk, 38:5 (1983), 199–200 | MR | Zbl

[10] Lychagin V. V., “Differentsialnye operatory na rassloennykh prostranstvakh”, Uspekhi matem. nauk, 40:2 (1985), 187–188 | MR | Zbl

[11] Seminar “Sofus Li”. Teoriya algebr Li. Topologiya grupp Li, IL, M., 1962

[12] Serr Zh.-P., “Lokalnaya algebra i teoriya kratnostei”, Matematika, 7:5 (1963), 3–93

[13] Spenser D., “Pereopredelennye sistemy differentsialnykh uravnenii v chastnykh proizvodnykh”, Matematika, 14:2 (1970), 66–90

[14] Fuks D. B., Kogomologii beskonechnomernykh algebr Li, Nauka, M., 1984 | MR | Zbl

[15] Hermann R., “The formal linearization of the semi-simple Lie algebra of vector fields about a singular point”, Trans. Amer. Math. Soc., 130 (1968), 105–109 | DOI | MR | Zbl

[16] Chen K. T., “Equivalence and decomposition of vector fields about an elementary critical point”, Amer. J. Math., 85 (1968), 693–722 | DOI | MR

[17] Guillemin V., Sternberg S., “Remarks on a paper of Hermann”, Trans. Amer. Math. Soc., 130 (1968), 110–116 | DOI | MR | Zbl

[18] Oshima T., “Singularities in contact geometry and degenerable pseudo-differential equations”, Jour. of the Faculty of Sci. Univ. Tokyo, Ser. I, 21:1 (1974), 43–83 | MR | Zbl