COMPLETELY AND PARTIALLY INTEGRABLE HAMILTONIAN SYSTEMS IN THE NONCOMPACT CASE

DOI10.1142/S0219887804000113zbMath1138.37323OpenAlexW1993493927MaRDI QIDQ4678264

Emanuele Fiorani

Publication date: 23 May 2005

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

Full work available at URL: https://doi.org/10.1142/s0219887804000113

zbMATH Keywords

Hamiltonian systemshomogeneous formalismCompletely and partially integrablesymplectically complete foliations

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45)

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Global action-angle coordinates for completely integrable systems with noncompact invariant submanifolds ⋮ Application of homotopy analysis method to option pricing under Lévy processes ⋮ The Poincaré-Lyapunov-Nekhoroshev theorem for involutory systems of vector fields ⋮ Speed and biases of Fourier-based pricing choices: a numerical analysis

Cites Work

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• The Poincaré-Lyapounov-Nekhoroshev theorem
• Compatibility of symplectic structures adapted to noncommutatively integrable systems
• The Euler-Poinsot top: a non-commutatively integrable system without global action-angle coordinates
• The Poincaré-Lyapunov-Liouville-Arnol'd theorem
• Quasi-periodicity of motions and complete integrability of Hamiltonian systems
• The Liouville Arnold Nekhoroshev theorem for non-compact invariant manifolds
• Geometric quantization of time-dependent completely integrable Hamiltonian systems

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