  Motivated by the time-dependent Hamiltonian dynamics, we extend the notion of
Arnold-Liouville and noncommutative integrability of Hamiltonian systems on
symplectic manifolds to that on cosymplectic manifolds. We prove a variant of
the non-commutative integrability for evaluation and Reeb vector fields on
cosymplectic manifolds and provide a construction of cosymplectic action-angle
variables.
