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

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

2001-06-04

arxiv.org/abs/math/0106013v1

Compositio Mathematica 101 (1996), 179-215

Mathematics

Dynamical Systems

Old paper put here for archival purposes. Contains a list of errata. 32 pages (=37 pages in Compositio), 1 figure

Scientific paper

The 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.

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