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Torus Actions and Integrable Systems

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arxiv math/0407455 v1 pith:JJXRRUPP submitted 2004-07-27 math.DS math-phmath.MP

Nguyen Tien Zung This is my paper · ORCID
classification math.DSmath-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. Full citation record

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

    math-ph 2025-07 unverdicted novelty 7.0 of 10

    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. Collective superintegrable systems from the Guillemin--Sternberg torus action

    math-ph 2026-08 conditional novelty 5.0 of 10

    Collective Hamiltonians of any Hamiltonian action of a compact semisimple Lie group form a superintegrable system, with action variables given by the Guillemin-Sternberg torus momentum map.

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