On the Birkhoff normal form of a completely integrable hamiltonian system near a fixed point with resonance
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 26 (1998) no. 4, p. 623-661
@article{ASNSP_1998_4_26_4_623_0,
     author = {Kappeler, Thomas and Kodama, Yuji and N\'emethi, Andr\'as},
     title = {On the Birkhoff normal form of a completely integrable hamiltonian system near a fixed point with resonance},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 26},
     number = {4},
     year = {1998},
     pages = {623-661},
     zbl = {0919.58030},
     mrnumber = {1648558},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1998_4_26_4_623_0}
}
Kappeler, Thomas; Kodama, Yuji; Némethi, Andras. On the Birkhoff normal form of a completely integrable hamiltonian system near a fixed point with resonance. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 26 (1998) no. 4, pp. 623-661. http://www.numdam.org/item/ASNSP_1998_4_26_4_623_0/

[Ar1] V.I. Arnold, "Mathematical methods of classical mechanics", 2nd ed., Springer, 1989. | MR 997295

[Ar2] V. I. ARNOLD (Ed.), "Dynamical systems III, Encycl. Math. Sci.", vol. 3, Springer, 1988. | MR 923953

[CB] R.H. Cushman - L.M. Bates, "Global Aspects of Classical Integrable Systems", Birkhäuser, 1997. | MR 1438060 | Zbl 0882.58023

[Du] J.J. Duistermaat, On global action-angle coordinates, Comm. Pure Appl. Math. 33 (1980), 687-706. | MR 596430 | Zbl 0439.58014

[El] H. Eliasson, Normal form of Hamiltonian systems with Poisson commuting integrals- elliptic case, Comment. Math. Helv. 65 (1990), 4-35. | MR 1036125 | Zbl 0702.58024

[Fo] A.T. Fomenko (Ed.), "Topological Classification of Integrable Systems", Adv. in Soviet Math. 6 AMS (1991). | MR 1141218 | Zbl 0741.00026

[GR] H. Grauert - R. Remmert, "Theory of Stein Spaces", Grundl. Math. Wiss. 236, Springer-Verlag, 1979. | MR 580152 | Zbl 0433.32007

[Hi] M. Hirsch, "Differential Topology", Graduate Text in Mathematics, Springer-Verlag, 1976. | MR 448362 | Zbl 0356.57001

[It1 ] H. Ito, Convergence of Birkhoff normal forms for integrable systems, Comment. Math. Helv. 64 (1989), 363-407. | MR 998858 | Zbl 0686.58021

[It2] H. Ito, Integrability of Hamiltonian systems and Birkhoff normal forms in the simple resonance case, Math. Ann. 292 (1992), 411-444. | MR 1152944 | Zbl 0735.58022

[It3] H. Ito, Action-angle coordinates at singularities for analytic integrable systems, Math. Z. 206 (1991), 363-407. | MR 1095762 | Zbl 0707.58026

[KK] L. Kaup - B. Kaup, "Holomorphic functions of several variables", de Gruyter Studies in Mathematics 3, Walter de Gruyter, Berlin- NewYork, 1983. | MR 716497 | Zbl 0528.32001

[Lo] E.J.N. Looijenga, "Isolated singular points on complete intersections", Cambridge University Press, 1984. | MR 747303 | Zbl 0552.14002

[Ma1] M. Marcus, "Finite dimensional multilinear algebra", M. Dekker, New York, 1973. | MR 352112

[Ma2] M. Marcus, "Finite dimensional multilinear algebra, Part 2", M. Dekker, New York, 1975. | MR 401796 | Zbl 0339.15003

[Mo] J. Moser, "Lectures on Hamiltonian systems", Memoir AMS, vol. 81, 1968. | MR 230498 | Zbl 0172.11401

[Sb] Y. Sibuya, "Linear differential equations in the complex domain: problems of analytic continuation", vol. 82, Translations of mathematical monographs AMS, 1990. | MR 1084379 | Zbl 00048899

[Si] C.L. Siegel, On the integrals of canonical systems, Ann. of Math. 42 (1941), 806-822. | JFM 67.0768.01 | MR 5818 | Zbl 0025.26503

[Ve] J. Vey, Sur certain systèmes dynamiques séparables, Amer. J. Math. 100 (1978), 591-614. | MR 501141 | Zbl 0384.58012