On the Birkhoff normal form of a completely integrable hamiltonian system near a fixed point with resonance
Thomas Kappeler; Yuji Kodama; Andras Némethi
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1998)
- Volume: 26, Issue: 4, page 623-661
- ISSN: 0391-173X
Access Full Article
topHow to cite
topKappeler, Thomas, Kodama, Yuji, and 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 26.4 (1998): 623-661. <http://eudml.org/doc/84341>.
@article{Kappeler1998,
author = {Kappeler, Thomas, Kodama, Yuji, Némethi, Andras},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {completely integrable Hamiltonian system; equilibrium point; Birkhoff normal form; simple resonance},
language = {eng},
number = {4},
pages = {623-661},
publisher = {Scuola normale superiore},
title = {On the Birkhoff normal form of a completely integrable hamiltonian system near a fixed point with resonance},
url = {http://eudml.org/doc/84341},
volume = {26},
year = {1998},
}
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
PB - Scuola normale superiore
VL - 26
IS - 4
SP - 623
EP - 661
LA - eng
KW - completely integrable Hamiltonian system; equilibrium point; Birkhoff normal form; simple resonance
UR - http://eudml.org/doc/84341
ER -
References
top- [Ar1] V.I. Arnold, "Mathematical methods of classical mechanics", 2nd ed., Springer, 1989. MR997295
- [Ar2] V. I. ARNOLD (Ed.), "Dynamical systems III, Encycl. Math. Sci.", vol. 3, Springer, 1988. MR923953
- [CB] R.H. Cushman - L.M. Bates, "Global Aspects of Classical Integrable Systems", Birkhäuser, 1997. Zbl0882.58023MR1438060
- [Du] J.J. Duistermaat, On global action-angle coordinates, Comm. Pure Appl. Math.33 (1980), 687-706. Zbl0439.58014MR596430
- [El] H. Eliasson, Normal form of Hamiltonian systems with Poisson commuting integrals- elliptic case, Comment. Math. Helv.65 (1990), 4-35. Zbl0702.58024MR1036125
- [Fo] A.T. Fomenko (Ed.), "Topological Classification of Integrable Systems", Adv. in Soviet Math.6AMS (1991). Zbl0741.00026MR1141218
- [GR] H. Grauert - R. Remmert, "Theory of Stein Spaces", Grundl. Math. Wiss.236, Springer-Verlag, 1979. Zbl0433.32007MR580152
- [Hi] M. Hirsch, "Differential Topology", Graduate Text in Mathematics, Springer-Verlag, 1976. Zbl0356.57001MR448362
- [It1 ] H. Ito, Convergence of Birkhoff normal forms for integrable systems, Comment. Math. Helv.64 (1989), 363-407. Zbl0686.58021MR998858
- [It2] H. Ito, Integrability of Hamiltonian systems and Birkhoff normal forms in the simple resonance case, Math. Ann.292 (1992), 411-444. Zbl0735.58022MR1152944
- [It3] H. Ito, Action-angle coordinates at singularities for analytic integrable systems, Math. Z.206 (1991), 363-407. Zbl0707.58026MR1095762
- [KK] L. Kaup - B. Kaup, "Holomorphic functions of several variables", de Gruyter Studies in Mathematics 3, Walter de Gruyter, Berlin- NewYork, 1983. Zbl0528.32001MR716497
- [Lo] E.J.N. Looijenga, "Isolated singular points on complete intersections", Cambridge University Press, 1984. Zbl0552.14002MR747303
- [Ma1] M. Marcus, "Finite dimensional multilinear algebra", M. Dekker, New York, 1973. MR352112
- [Ma2] M. Marcus, "Finite dimensional multilinear algebra, Part 2", M. Dekker, New York, 1975. Zbl0339.15003MR401796
- [Mo] J. Moser, "Lectures on Hamiltonian systems", Memoir AMS, vol. 81, 1968. Zbl0172.11401MR230498
- [Sb] Y. Sibuya, "Linear differential equations in the complex domain: problems of analytic continuation", vol. 82, Translations of mathematical monographsAMS, 1990. Zbl1145.34378MR1084379
- [Si] C.L. Siegel, On the integrals of canonical systems, Ann. of Math.42 (1941), 806-822. Zbl0025.26503MR5818JFM67.0768.01
- [Ve] J. Vey, Sur certain systèmes dynamiques séparables, Amer. J. Math.100 (1978), 591-614. Zbl0384.58012MR501141
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.