On Linearized Poisson Structures
Matematičeskie zametki, Tome 70 (2001) no. 4, pp. 535-543.

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

It is shown that, up to a diffeomorphism, the linearized Poisson structure does not depend on the choice of the transversal near the zero section.
@article{MZM_2001_70_4_a4,
     author = {Yu. M. Vorob'ev},
     title = {On {Linearized} {Poisson} {Structures}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {535--543},
     publisher = {mathdoc},
     volume = {70},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a4/}
}
TY  - JOUR
AU  - Yu. M. Vorob'ev
TI  - On Linearized Poisson Structures
JO  - Matematičeskie zametki
PY  - 2001
SP  - 535
EP  - 543
VL  - 70
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a4/
LA  - ru
ID  - MZM_2001_70_4_a4
ER  - 
%0 Journal Article
%A Yu. M. Vorob'ev
%T On Linearized Poisson Structures
%J Matematičeskie zametki
%D 2001
%P 535-543
%V 70
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a4/
%G ru
%F MZM_2001_70_4_a4
Yu. M. Vorob'ev. On Linearized Poisson Structures. Matematičeskie zametki, Tome 70 (2001) no. 4, pp. 535-543. http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a4/

[1] Weinstein A., “The local structure of Poisson manifolds”, J. Differential Geom., 18 (1983), 523–557 | MR | Zbl

[2] Conn J., “Normal forms for analytic Poisson structures”, Ann. of Math., 119 (1984), 576–601 | DOI | MR

[3] Conn J., “Normal forms for smooth Poisson structures”, Ann. of Math., 121 (1985), 565–593 | DOI | MR | Zbl

[4] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1989

[5] Dufour J.-P., Quadratiation de structures de Poisson à partie quadratuque diagonale, Seminaire Gaston Darboux de Geometrie et Topologie Differentielle, Univ. Montpellier II, Montpellier, 1994

[6] Karasev M. V., Vorobjev Yu. M., “Deformations and cohomology of Poisson manifolds”, Lecture Notes in Math., 1453, Springer-Verlag, Berlin, 1990, 271–289 | MR

[7] Itskov V. M., Karasev M. V., Vorobjev Yu. M., “Infinitesimal Poisson geometry”, Amer. Math. Soc. Transl. (2), 187 (1998), 327–360 | MR | Zbl

[8] Sternberg S., “Minimal coupling and the symplectic mechanics of a classical particle in the presence of a Young–Mills field”, Proc. Nat. Acad. Sci. USA, 74 (1977), 5253–5254 | DOI | MR | Zbl

[9] Montgomery R., “Canonical formalism of a classical particle in a Yang–Mills field and Wong's equations”, Let. Math. Phys., 8 (1984), 59–67 | DOI | MR | Zbl

[10] Guillemin V., Sternberg S., Symplectic Technique in Physics, Cambridge Univ. Press, Cambridge, 1984 | Zbl

[11] Vorobjev Yu. V., Coupling Tensors and Poisson Geometry near a Single Symplectic Leaf, {http://arxiv.org/abs/math/0008162}{E-print math.SG/0008097}, 2000

[12] Karasev M. V., Maslov V. P., Nelineinye skobki Puassona. Geometriya i kvantovanie, Nauka, M., 1991 | Zbl