Geodesic
Versal deformations of differential forms of real degree on the real line
Izvestiya. Mathematics, Tome 37 (1991) no. 3, pp. 525-537 
V. P. Kostov. Versal deformations of differential forms of real degree on the real line. Izvestiya. Mathematics, Tome 37 (1991) no. 3, pp. 525-537. http://geodesic.mathdoc.fr/item/IM2_1991_37_3_a3/
@article{IM2_1991_37_3_a3,
     author = {V. P. Kostov},
     title = {Versal deformations of differential forms of real degree on the real line},
     journal = {Izvestiya. Mathematics},
     pages = {525--537},
     year = {1991},
     volume = {37},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1991_37_3_a3/}
}
TY  - JOUR
AU  - V. P. Kostov
TI  - Versal deformations of differential forms of real degree on the real line
JO  - Izvestiya. Mathematics
PY  - 1991
SP  - 525
EP  - 537
VL  - 37
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/IM2_1991_37_3_a3/
LA  - en
ID  - IM2_1991_37_3_a3
ER  - 
%0 Journal Article
%A V. P. Kostov
%T Versal deformations of differential forms of real degree on the real line
%J Izvestiya. Mathematics
%D 1991
%P 525-537
%V 37
%N 3
%U http://geodesic.mathdoc.fr/item/IM2_1991_37_3_a3/
%G en
%F IM2_1991_37_3_a3

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

A normal form is given for families of differential forms of nonzero real degree on the real line (in particular, a normal form for families of vector fields on the line), which depend smoothly on the parameters, in the neighborhood of zeros of the coefficient of the form of finite multiplicity (zeros of finite multiplicity of the field).

[1] Arnold V. I., Varchenko A. N., Gusein-Zade S. M., Osobennosti differentsiruemykh otobrazhenii. Klassifikatsiya kriticheskikh tochek, kaustik i volnovykh frontov, t. 1, Nauka, M., 1982 | MR

[2] Arnold V. I., “Osobennosti v variatsionnom ischislenii”, Itogi nauki i tekhniki: Sovremennye problemy matematiki, 22, VINITI, M., 1983, 3–55

[3] Givental A. B., “Lagranzhevy mnogoobraziya s osobennostyami i neprivodimye $sl_x$-moduli”, UMN, 38:6 (1983), 109–110 | MR | Zbl

[4] Kostov V. P., “Versalnye deformatsii differentsialnykh form stepeni $\alpha$ na pryamoi”, Funkts. analiz i ego prilozh., 18:4 (1984), 81–82 | MR | Zbl

[5] Takens F., “Normal Forms for Certain Singularities of Vectorfields”, Ann. Inst. Fourier, 23:2 (1973), 163–195 | MR | Zbl

[6] Kuznetsov A. N., “Differentsiruemye resheniya vyrozhdayuschikhsya sistem”, Funkts. analiz i ego prilozh., 6:2 (1972), 41–51 | MR | Zbl

[7] Martinet J., “Deploiments Versels des Applications Differentiables et Classification des Applications Stables”, Lecture Notes in Mathematics, 535, 1976, 1–44 | MR | Zbl

[8] Golubitskii M., Giiemin V., Ustoichivye otobrazheniya i ikh osobennosti, Mir, M., 1977 | MR