  We consider Noether symmetries within Hamiltonian setting as transformations
that preserve Poincar\'e-Cartan form, i.e., as symmetries of characteristic
line bundles of nondegenerate 1-forms. In the case when the Poincar\'e-Cartan
form is contact, the explicit expression for the symmetries in the inverse
Noether theorem is given. As examples, we consider natural mechanical systems,
in particular the Kepler problem. Finally, we prove a variant of the theorem on
complete (non-commutative) integrability in terms of Noether symmetries of
time-dependent Hamiltonian systems.
