  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.
