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Monnier, Philippe; Zung, Nguyen Tien
Normal forms of vector fields on Poisson manifolds. Annales mathématiques Blaise Pascal, 13 no. 2 (2006), p. 349-380
Texte intégral djvu | pdf | Analyses MR 2275451 | Zbl 05127368
URL stable: http://www.numdam.org/item?id=AMBP_2006__13_2_349_0
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We study formal and analytic normal forms of radial and Hamiltonian vector fields on Poisson manifolds near a singular point.
[1] G.D. Birkhoff, Dynamical Systems, AMS Colloq. Publ., 1927 JFM 53.0732.01
[2] A.D. Bruno, Analytic form of differential equations, Trans. Moscow Math. Soc., 25:131-288, 1971 Zbl 0272.34018
[3] A.D. Bruno, Local methods in nonlinear differential equations, Springer-Verlag, 1989 MR 993771 | Zbl 0674.34002
[4] J. Conn, Normal forms for analytic Poisson structures, Ann. of Math., 119:577-601, 1984 MR 744864 | Zbl 0553.58004
[5] P. Dazord, A. Lichnerowicz and Ch.-M. Marle, Structure locale des variétés de Jacobi, J. Math. Pures Appl., 70:101-152, 1991 MR 1091922 | Zbl 0659.53033
[6] J.-P. Dufour and N. T. Zung, Poisson structures and their normal forms, Birkhauser Verlag, 2005 MR 2178041 | Zbl 02237399
[7] V. Ginzburg, Momentum mappings and Poisson cohomology, Internat. J. Math., 7:329-358, 1996 MR 1395934 | Zbl 0867.58028
[8] A.W. Knapp, Lie groups beyond an introduction, Birkhauser, 2002 MR 1920389 | Zbl 1075.22501
[9] E. Miranda and N.T. Zung, Equivariant normal forms of Poisson structures, 2005
arXiv
[10] C.L. Siegel and J. Moser, Lectures on celestial mechanics, Springer-Verlag, 1971 MR 502448 | Zbl 0817.70001
[11] I. Vaisman, Lectures on the Geometry of Poisson Manifolds, Birkhauser Verlag, 1994 MR 1269545 | Zbl 0810.53019
[12] A. Weinstein, The local structure of Poisson manifolds, J. Differential Geom., 18:523-557, 1983 MR 723816 | Zbl 0524.58011
[13] N.T. Zung, Convergence versus integrability in Poincaré-Dulac normal forms, Math. Res. Lett., 9:217-228, 2002 MR 1909639 | Zbl 1019.34084
[14] N.T. Zung, Torus action and integrable systems, 2004
arXiv
[15] N.T. Zung, Convergence versus integrability in Birkhoff normal forms, Ann. of Math., 161:139-154, 2005 MR 2150385 | Zbl 1076.37045
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