Geodesic
Classification of simple multigerms of curves in the contact space
Algebra i analiz, Tome 18 (2006) no. 2, pp. 80-116.

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

Stably simple singularities of curves (both reducible and irreducible) in the contact complex space are classified up to formal stable contact equivalence.The classification widens the one obtained by V. I. Arnold in 1999 for the simple contact space singularities that are RL-equivalent to the singularity A2 (a semicubical parabola). The proofs involve the homotopy method and the Darboux-Givental theorem on contact structures. 
@article{AA_2006_18_2_a3,
     author = {P. A. Kolgushkin},
     title = {Classification of simple multigerms of curves in the contact space},
     journal = {Algebra i analiz},
     pages = {80--116},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2006},
     language = {ru},
     url = {https://geodesic-test.mathdoc.fr/item/AA_2006_18_2_a3/}
}
TY  - JOUR
AU  - P. A. Kolgushkin
TI  - Classification of simple multigerms of curves in the contact space
JO  - Algebra i analiz
PY  - 2006
SP  - 80
EP  - 116
VL  - 18
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/AA_2006_18_2_a3/
LA  - ru
ID  - AA_2006_18_2_a3
ER  - 
%0 Journal Article
%A P. A. Kolgushkin
%T Classification of simple multigerms of curves in the contact space
%J Algebra i analiz
%D 2006
%P 80-116
%V 18
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/AA_2006_18_2_a3/
%G ru
%F AA_2006_18_2_a3
P. A. Kolgushkin. Classification of simple multigerms of curves in the contact space. Algebra i analiz, Tome 18 (2006) no. 2, pp. 80-116. https://geodesic-test.mathdoc.fr/item/AA_2006_18_2_a3/

[1] Bruce J. W., Gaffney T. J., “Simple singularities of mappings $(\mathbb C,0)\to(\mathbb C^2,0)$”, J. London Math. Soc. (2), 26 (1982), 465–474 | DOI | MR | Zbl

[2] Gibson C. G., Hobbs C. A., “Simple singularities of space curves”, Math. Proc. Cambridge Philos. Soc., 113:2 (1993), 297–310 | DOI | MR | Zbl

[3] Arnold V. I., “Prostye osobennosti krivykh”, Tr. Mat. in-ta RAN, 226, 1999, 27–35 | MR | Zbl

[4] Kolgushkin P. A., Sadykov R. R., “Klassifikatsiya prostykh multirostkov krivykh”, Uspekhi mat. nauk, 56:6 (2001), 153–154 | MR | Zbl

[5] Kolgushkin P. A., Sadykov R. R., “Simple singularities of multigerms of curves”, Rev. Mat. Complut., 14:2 (2001), 311–344 ; см. также препринт math.AG/0012040 | MR | Zbl

[6] Arnold V. I., “First steps of local symplectic algebra”, Differential Topology, Infinite-Dimensional Lie Algebras, and Applications, Amer. Math. Soc. Transl. Ser. 2, 194, Amer. Math. Soc., Providence, RI, 1999, 1–8 | MR | Zbl

[7] Kolgushkin P. A., “Klassifikatsiya prostykh multirostkov krivykh v prostranstve, snabzhennom simplekticheskoi strukturoi”, Algebra i analiz, 15:1 (2003), 148–183 | MR | Zbl

[8] Arnold V. I., “First steps of local contact algebra”, Canad. J. Math., 51:6 (1999), 1123–1134 | MR | Zbl

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

[10] Arnold V. I., Givental A. B., Simplekticheskaya geometriya, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. napravleniya, 4, M., 1985, 5–139 | MR