GEOMETRICAL ASPECTS OF INTEGRABLE SYSTEMS

DOI10.1142/S0219887808002886zbMath1176.70013arXiv0802.1905MaRDI QIDQ3520380

Emanuele Fiorani

Publication date: 26 August 2008

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.1905

zbMATH Keywords

Integrable Hamiltonian systemsglobal action-nagle coordinateslocally affine structures

Mathematics Subject Classification ID

Hamilton's equations (70H05) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65)

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Cites Work

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• The Poincaré-Lyapounov-Nekhoroshev theorem
• Generalized Liouville method of integration of Hamiltonian systems
• The Poincaré-Lyapunov-Liouville-Arnol'd theorem
• Superintegrable Hamiltonian systems: Geometry and perturbations
• Noncommutative integrability on noncompact invariant manifolds
• Global action-angle coordinates for completely integrable systems with noncompact invariant submanifolds
• On global action-angle coordinates
• Submersions, fibrations and bundles
• Geometric quantization of time-dependent completely integrable Hamiltonian systems
• Bi-Hamiltonian partially integrable systems

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