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This article is cited in 12 scientific papers (total in 12 papers)
JÜRGEN MOSER – 80
Global properties of integrable Hamiltonian systems
F. Takens, H. W. Broer, O. V. Lukina Institute for Mathematics and Computer Science, University of Groningen
P.O. Box 407, 9700 AK Groningen, The Netherlands
Abstract:
This paper deals with Lagrangian bundles which are symplectic torus bundles that occur in integrable Hamiltonian systems. We review the theory of obstructions to triviality, in particular monodromy, as well as the ensuing classification problems which involve the Chern and Lagrange class. Our approach, which uses simple ideas from differential geometry and algebraic topology, reveals the fundamental role of the integer affine structure on the base space of these bundles. We provide a geometric proof of the classification of Lagrangian bundles with fixed integer affine structure by their Lagrange class.
Keywords:
integrable Hamiltonian system, global action-angle coordinates, symplectic topology, monodromy, Lagrange class, classification of integrable systems.
Received: 31.05.2008 Accepted: 22.08.2008
Citation:
F. Takens, H. W. Broer, O. V. Lukina, “Global properties of integrable Hamiltonian systems”, Regul. Chaotic Dyn., 13:6 (2008), 602–644
Linking options:
https://www.mathnet.ru/eng/rcd605 https://www.mathnet.ru/eng/rcd/v13/i6/p602
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