Normal forms of vector fields on Poisson manifolds
Annales mathématiques Blaise Pascal, Tome 13 (2006) no. 2, pp. 349-380.

We study formal and analytic normal forms of radial and Hamiltonian vector fields on Poisson manifolds near a singular point.

DOI : 10.5802/ambp.221
Monnier, Philippe 1 ; Zung, Nguyen Tien 1

1 Laboratoire Emile Picard Université Paul Sabatier 31062 Toulouse Cedex *9 FRANCE
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Monnier, Philippe; Zung, Nguyen Tien. Normal forms of vector fields on Poisson manifolds. Annales mathématiques Blaise Pascal, Tome 13 (2006) no. 2, pp. 349-380. doi : 10.5802/ambp.221. http://archive.numdam.org/articles/10.5802/ambp.221/

[1] Birkhoff, G.D. Dynamical Systems, AMS Colloq. Publ., Providence, 1927

[2] Bruno, A.D. Analytic form of differential equations, Trans. Moscow Math. Soc., Volume 25 (1971), pp. 131-288 | Zbl

[3] Bruno, A.D. Local methods in nonlinear differential equations, Springer-Verlag, Berlin, 1989 | MR | Zbl

[4] Conn, J. Normal forms for analytic Poisson structures, Ann. of Math., Volume 119 (1984), pp. 577-601 | DOI | MR | Zbl

[5] Dazord, P.; Lichnerowicz, A.; Marle, Ch.-M. Structure locale des variétés de Jacobi, J. Math. Pures Appl., Volume 70 (1991), pp. 101-152 | MR | Zbl

[6] Dufour, J.-P.; Zung, N. T. Poisson structures and their normal forms, Birkhauser Verlag, Basel, 2005 | MR | Zbl

[7] Ginzburg, V. Momentum mappings and Poisson cohomology, Internat. J. Math., Volume 7 (1996), pp. 329-358 | DOI | MR | Zbl

[8] Knapp, A.W. Lie groups beyond an introduction, Birkhauser, Boston, 2002 | MR | Zbl

[9] Miranda, E.; Zung, N.T. Equivariant normal forms of Poisson structures (2005) (math.SG/0510523)

[10] Siegel, C.L.; Moser, J. Lectures on celestial mechanics, Springer-Verlag, New York - Heidelberg, 1971 | MR | Zbl

[11] Vaisman, I. Lectures on the Geometry of Poisson Manifolds, Birkhauser Verlag, Basel, 1994 | MR | Zbl

[12] Weinstein, A. The local structure of Poisson manifolds, J. Differential Geom., Volume 18 (1983), pp. 523-557 | MR | Zbl

[13] Zung, N.T. Convergence versus integrability in Poincaré-Dulac normal forms, Math. Res. Lett., Volume 9 (2002), pp. 217-228 | MR | Zbl

[14] Zung, N.T. Torus action and integrable systems (2004) (math.DS/0407455)

[15] Zung, N.T. Convergence versus integrability in Birkhoff normal forms, Ann. of Math., Volume 161 (2005), pp. 139-154 | DOI | MR | Zbl

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