Geodesic
Linéarisation symplectique en dimension 2
Canadian mathematical bulletin, Tome 44 (2001) no. 2, pp. 129-139

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper the germ of neighborhood of a compact leaf in a Lagrangian foliation is symplectically classified when the compact leaf is ${{\mathbb{T}}^{2}}$ , the affine structure induced by the Lagrangian foliation on the leaf is complete, and the holonomy of ${{\mathbb{T}}^{2}}$ in the foliation linearizes. The germ of neighborhood is classified by a function, depending on one transverse coordinate, this function is related to the affine structure of the nearly compact leaves.
DOI : 10.4153/CMB-2001-017-2
Mots-clés : 53C12, 58F05, symplectic manifold, Lagrangian foliation, affine connection 
Currás-Bosch, Carlos. Linéarisation symplectique en dimension 2. Canadian mathematical bulletin, Tome 44 (2001) no. 2, pp. 129-139. doi: 10.4153/CMB-2001-017-2
@article{10_4153_CMB_2001_017_2,
     author = {Curr\'as-Bosch, Carlos},
     title = {Lin\'earisation symplectique en dimension 2},
     journal = {Canadian mathematical bulletin},
     pages = {129--139},
     year = {2001},
     volume = {44},
     number = {2},
     doi = {10.4153/CMB-2001-017-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2001-017-2/}
}
TY  - JOUR
AU  - Currás-Bosch, Carlos
TI  - Linéarisation symplectique en dimension 2
JO  - Canadian mathematical bulletin
PY  - 2001
SP  - 129
EP  - 139
VL  - 44
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2001-017-2/
DO  - 10.4153/CMB-2001-017-2
ID  - 10_4153_CMB_2001_017_2
ER  - 
%0 Journal Article
%A Currás-Bosch, Carlos
%T Linéarisation symplectique en dimension 2
%J Canadian mathematical bulletin
%D 2001
%P 129-139
%V 44
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2001-017-2/
%R 10.4153/CMB-2001-017-2
%F 10_4153_CMB_2001_017_2

[1] [1] Currás-Bosch, C., Sur les feuilletages Lagrangiens `a holonomie linéaire. C. R. Acad. Sci. Paris 317 (1993), 605–608. Google Scholar

[2] [2] Currás-Bosch, C. et Molino, P., Voisinage d’une feuille compacte dans un feuilletage Lagrangien: le problème de linéarisation symplectique. Hokkaido Math. J. 23 (1994), 355–360. Google Scholar

[3] [3] Currás-Bosch, C. et Molino, P., Réduction symplectique d’un feuilletage Lagrangien au voisinage d’une feuille compacte. C. R. Acad. Sci. Paris 318 (1994), 661–664. Google Scholar

[4] [4] Currás-Bosch, C. et Molino, P., Un exemple de classification de germes de feuilletages Lagrangiens au voisinage d’une feuille compacte. Indag.Math. (N.S.) (2) 19 (1998), 197–209. Google Scholar

[5] [5] Dazord, P., Sur la géométrie des sous-fibrés et des feuilletages Lagrangiens. Ann. Sci. École Norm. Sup. 4 14 (1981), 465–480. Google Scholar

[6] [6] Kuiper, N. H., Sur les surfaces localement affines. Colloque de Géométrie Différentielle (Strasbourg, 1953), Centre National de la Recherche Scientifique, Paris, 1953, 79–87. Google Scholar

[7] [7] Libermann, P. et Marle, Ch. M., Symplectic Geometry and Analytical Mechanics. D. Reidel Publishing Company, 1987. Google Scholar

[8] [8] Molino, P., Exposés au Séminaire Sud-Rhodanien. Avignon, 1990, et Marseille, 1990. Google Scholar

[9] [9] Nagano, T. et Yagi, K., The affine structures on the real two torus. Osaka J. Math. 11 (1974), 181–210. Google Scholar

[10] [10] Weinstein, A., Lectures on symplectic manifolds. Regional Conference Series in Mathematics 29, Amer. Math. Soc., Providence, RI, 1977. Google Scholar

[11] [11] Weinstein, A., Symplectic manifolds and their Lagrangian submanifolds. Adv. Math. 6 (1971), 329–346. Google Scholar

Cité par Sources :