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Torus actions and integrable systems. (English) Zbl 1329.37054

Bolsinov, A. V. et al., Topological methods in the theory of integrable systems. Cambridge: Cambridge Scientific Publishers (ISBN 978-1-904868-42-2/hbk). 289-328 (2006).
Summary: This is a survey on natural local torus actions which arise in integrable dynamical systems, and their relations with other subjects, including: reduced integrability, local normal forms, affine structures, monodromy, global invariants, integrable surgery, convexity properties of momentum maps, localization formulas, integrable PDEs.
For the entire collection see [Zbl 1142.37001].

MSC:

37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
37G05 Normal forms for dynamical systems
53D20 Momentum maps; symplectic reduction
70H05 Hamilton’s equations
70K45 Normal forms for nonlinear problems in mechanics
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