We prove that the singular Lagrangian foliation of a 2-degree of freedom integrable Hamiltonian system, is
symplectically equivalent to the linearized foliation in a neighbourhood of a non-degenerate singular orbit.
Curras-Bosch, C.; Miranda, E. Symplectic linearization of singular Lagrangian foliations in M4. "Differential geometry and its applications", Març 2003, vol. 18, núm. 2, p. 195-205.