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arxiv: math/0407455 · v1 · submitted 2004-07-27 · 🧮 math.DS · math-ph· math.MP

Torus Actions and Integrable Systems

Nguyen Tien Zung This is my paper
classification 🧮 math.DS math-phmath.MP
keywords integrableactionslocalsystemstorusaffineariseconvexity
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Integrable systems from Poisson reductions of generalized Hamiltonian torus actions

    math-ph 2025-07 unverdicted novelty 6.0

    Develops sufficient conditions for Poisson reduction of generalized Hamiltonian torus actions to preserve integrability and applies them to open problems on Lie group doubles and flat-connection moduli spaces.

  2. Integrable systems from Poisson reductions of generalized Hamiltonian torus actions

    math-ph 2025-07 unverdicted novelty 6.0

    Develops sufficient conditions for integrable systems to descend under Poisson reductions of generalized Hamiltonian torus actions, with applications to systems on doubles of compact Lie groups and moduli spaces of fl...