Global Action-Angle Variables for Non-Commutative Integrable Systems

  title={Global Action-Angle Variables for Non-Commutative Integrable Systems},
  author={Rui Loja Fernandes and Camille Laurent-Gengoux and Pol Vanhaecke},
  journal={arXiv: Differential Geometry},
In this paper we analyze the obstructions to the existence of global action-angle variables for regular non-commutative integrable systems (NCI systems) on Poisson manifolds. In contrast with local action-angle variables, which exist as soon as the fibers of the momentum map of such an integrable system are compact, global action-angle variables rarely exist. This fact was first observed and analyzed by Duistermaat in the case of Liouville integrable systems on symplectic manifolds and later by… Expand
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  • Peter Crooks
  • Mathematics
  • Bulletin of the Australian Mathematical Society
  • 2018
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