A compact connected regular common level of commuting integrals is an -torus with local action-angle coordinates.
Articles by others on the same topic
The Liouville–Arnold theorem, also known as the Liouville–Arnold theorem of integrability, is a result in Hamiltonian mechanics concerning the integrability of Hamiltonian systems. It provides a criterion under which a dynamical system can be considered integrable in the sense of having as many conserved quantities as degrees of freedom, allowing the system to be solved in terms of action-angle variables.