Lesfari, A. The Arnold-Liouville theorem of and its consequences. (Le théorème d’Arnold-Liouville et ses conséquences.) (English) Zbl 1112.37043 Elem. Math. 58, No. 1, 6-20 (2003). 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. Reviewer: Ioan Bucataru (Iaşi) Cited in 6 Documents MSC: 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 70H06 Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics PDFBibTeX XMLCite \textit{A. Lesfari}, Elem. Math. 58, No. 1, 6--20 (2003; Zbl 1112.37043) Full Text: DOI