Nguyen Tien Zung 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]. Cited in 1 ReviewCited in 23 Documents 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 Keywords:integrable system; local torus actions; PoincarĂ©-Birkhoff normal form; reduced integrability; affine structure; monodromy, convexity; proper groupoid; localization formula PDFBibTeX XMLCite \textit{Nguyen Tien Zung}, in: Topological methods in the theory of integrable systems. Cambridge: Cambridge Scientific Publishers. 289--328 (2006; Zbl 1329.37054) Full Text: arXiv