Integrable systems on singular symplectic manifolds: from local to global
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hdl:2117/365678
Tipus de documentReport de recerca
Data publicació2021-02-03
Condicions d'accésAccés obert
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Abstract
In this article, we consider integrable systems on manifolds endowed with symplectic structures with singularities of order one. These structures are symplectic away from a hypersurface where the symplectic volume goes either to infinity or to zero transversally, yielding either a b-symplectic form or a folded symplectic form. The hypersurface where the form degenerates is called critical set. We give a new impulse to the investigation of the existence of action-angle coordinates for these structures initiated in [36] and [37] by proving an action-angle theorem for folded symplectic integrable systems. Contrary to expectations, the action-angle coordinate theorem for folded symplectic manifolds cannot be presented as a cotangent lift as done for symplectic and bsymplectic forms in [36]. Global constructions of integrable systems are provided and obstructions for the global existence of action-angle coordinates are investigated in both scenarios. The new topological obstructions found emanate from the topology of the critical set Z of the singular symplectic manifold. The existence of these obstructions in turn implies the existence of singularities for the integrable system on Z.
CitacióMiranda, E.; Cardona, R. Integrable systems on singular symplectic manifolds: from local to global. 2021.
Altres identificadorshttps://arxiv.org/abs/2007.10314
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Final_FoldedIntegrable_IMRN.pdf | 517,3Kb | Visualitza/Obre |