Symplectic topology of integrable Hamiltonian systems, I: Arnold-Liouville with singularities

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dc.creatorZung, Nguyen Tien
dc.date2001-06-04
dc.date.accessioned2026-07-07T04:41:57Z
dc.date.available2026-07-07T04:41:57Z
dc.descriptionThe classical Arnold-Liouville theorem describes the geometry of an integrable Hamiltonian system near a regular level set of the moment map. Our results describe it near a nondegenerate singular level set: a tubular neighborhood of a connected singular nondegenerate level set, after a normal finite covering, admits a non-complete system of action-angle functions (the number of action functions is equal to the rank of the moment map), and it can be decomposed topologically, together with the associated singular Lagrangian foliation, to a direct product of simplest (codimension 1 and codimension 2) singularities. These results are essential for the global topological study of integrable Hamiltonian systems.
dc.descriptionOld paper put here for archival purposes. Contains a list of errata. 32 pages (=37 pages in Compositio), 1 figure
dc.identifierhttps://arxiv.org/abs/math/0106013
dc.identifierhttp://arxiv.org/abs/math/0106013
dc.identifierCompositio Mathematica 101 (1996), 179-215
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61576
dc.subjectDynamical Systems
dc.subjectMathematical Physics
dc.subject58F07, 58F14, 58F05, 70H05
dc.titleSymplectic topology of integrable Hamiltonian systems, I: Arnold-Liouville with singularities
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