The Arnold-Liouville theorem of and its consequences. (Q1404163)

The author studies some consequences of the following result: a compact connected, \(n\)-dimensional manifold that admits n commuting, everywhere independent vector fields is dipheomorphic to an \(n\)-dimensional torus. Such result is applied in Section 2 to Hamiltonian mechanical systems. However, no requirement for the maximal rank of the matrix representation \(J\) of the Poisson structure is made.