Le problème général des variables actions-angles. (The general problem of action-angle variables). (English) Zbl 0634.58003

The paper is devoted to geometrical and topological classification of complete symplectic foliations arising in symplectic geometry, Hamiltonian mechanics, geometric quantization, etc. Isotropic symplectic complete fibrations are studied. Some results may be considered as a noncommutative generalization of V. I. Arnol’d’s theorem on action-angle variables. Certain other properties connected with these variables are obtained. Relations to results of V. I. Arnol’d, J. Duistermaat, A. Weinstein and a lot of other authors are discussed.
Reviewer: Yu.E.Gliklikh


37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
53D50 Geometric quantization
37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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