@article{ASNSP_1998_4_26_4_623_0, author = {Kappeler, Thomas and Kodama, Yuji and N\'emethi, Andras}, 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}, pages = {623--661}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 26}, number = {4}, year = {1998}, mrnumber = {1648558}, zbl = {0919.58030}, language = {en}, url = {http://www.numdam.org/item/ASNSP_1998_4_26_4_623_0/} }
TY - JOUR AU - Kappeler, Thomas AU - Kodama, Yuji AU - Némethi, Andras TI - On the Birkhoff normal form of a completely integrable hamiltonian system near a fixed point with resonance JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1998 SP - 623 EP - 661 VL - 26 IS - 4 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_1998_4_26_4_623_0/ LA - en ID - ASNSP_1998_4_26_4_623_0 ER -
%0 Journal Article %A Kappeler, Thomas %A Kodama, Yuji %A Némethi, Andras %T On the Birkhoff normal form of a completely integrable hamiltonian system near a fixed point with resonance %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1998 %P 623-661 %V 26 %N 4 %I Scuola normale superiore %U http://www.numdam.org/item/ASNSP_1998_4_26_4_623_0/ %G en %F 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, Serie 4, Volume 26 (1998) no. 4, pp. 623-661. http://www.numdam.org/item/ASNSP_1998_4_26_4_623_0/
[Ar1] "Mathematical methods of classical mechanics", 2nd ed., Springer, 1989. | MR
,[Ar2] V. I. ARNOLD (Ed.), "Dynamical systems III, Encycl. Math. Sci.", vol. 3, Springer, 1988. | MR
[CB] Global Aspects of Classical Integrable Systems", Birkhäuser, 1997. | MR | Zbl
- , "[Du] On global action-angle coordinates, Comm. Pure Appl. Math. 33 (1980), 687-706. | MR | Zbl
,[El] Normal form of Hamiltonian systems with Poisson commuting integrals- elliptic case, Comment. Math. Helv. 65 (1990), 4-35. | MR | Zbl
,[Fo] A.T. Fomenko (Ed.), "Topological Classification of Integrable Systems", Adv. in Soviet Math. 6 AMS (1991). | MR | Zbl
[GR] Theory of Stein Spaces", Grundl. Math. Wiss. 236, Springer-Verlag, 1979. | MR | Zbl
- , "[Hi] Differential Topology", Graduate Text in Mathematics, Springer-Verlag, 1976. | MR | Zbl
, "[It1 ] Convergence of Birkhoff normal forms for integrable systems, Comment. Math. Helv. 64 (1989), 363-407. | MR | Zbl
,[It2] Integrability of Hamiltonian systems and Birkhoff normal forms in the simple resonance case, Math. Ann. 292 (1992), 411-444. | MR | Zbl
,[It3] Action-angle coordinates at singularities for analytic integrable systems, Math. Z. 206 (1991), 363-407. | MR | Zbl
,[KK] "Holomorphic functions of several variables", de Gruyter Studies in Mathematics 3, Walter de Gruyter, Berlin- NewYork, 1983. | MR | Zbl
- ,[Lo] "Isolated singular points on complete intersections", Cambridge University Press, 1984. | MR | Zbl
,[Ma1] "Finite dimensional multilinear algebra", M. Dekker, New York, 1973. | MR
,[Ma2] Finite dimensional multilinear algebra, Part 2", M. Dekker, New York, 1975. | MR | Zbl
, "[Mo] "Lectures on Hamiltonian systems", Memoir AMS, vol. 81, 1968. | MR | Zbl
,[Sb] "Linear differential equations in the complex domain: problems of analytic continuation", vol. 82, Translations of mathematical monographs AMS, 1990. | MR | Zbl
,[Si] On the integrals of canonical systems, Ann. of Math. 42 (1941), 806-822. | JFM | MR | Zbl
,[Ve] Sur certain systèmes dynamiques séparables, Amer. J. Math. 100 (1978), 591-614. | MR | Zbl
,