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On the Birkhoff normal form of a completely integrable Hamiltonian system near a fixed point with resonance


Kappeler, T; Kodama, Y; Némethi, A (1998). 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 IV, 26(4):623-661.

Abstract

We consider an integrable Hamiltonian system with a real analytic Hamiltonian H near an elliptic fixed point P. If H has a simple resonance and admits a semisimple Hessian at P we show that there exists a real analytic change of coordinates which brings the Hamiltonian into normal form. In the new coordinates, the level sets of the system are analyzed in terms of the nature of the simple resonance.

We consider an integrable Hamiltonian system with a real analytic Hamiltonian H near an elliptic fixed point P. If H has a simple resonance and admits a semisimple Hessian at P we show that there exists a real analytic change of coordinates which brings the Hamiltonian into normal form. In the new coordinates, the level sets of the system are analyzed in terms of the nature of the simple resonance.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:completely integrable Hamiltonian system; equilibrium point; Birkhoff normal form; simple resonance
Language:English
Date:1998
Deposited On:18 Feb 2010 13:02
Last Modified:05 Apr 2016 13:26
Publisher:Scuola Normale Superiore di Pisa
ISSN:0391-173X
Additional Information:© 1998 Scuola Normale Superiore di Pisa
Official URL:http://www.numdam.org/item?id=ASNSP_1998_4_26_4_623_0
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1648558
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0919.58030
Permanent URL: http://doi.org/10.5167/uzh-22206

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