  The notion of integrability is discussed for classical nonautonomous systems
with one degree of freedom. The analysis is focused on models which are
linearly spanned by finite Lie algebras. By constructing the autonomous
extension of the time-dependent Hamiltonian we prove the existence of two
invariants in involution which are shown to obey the criterion of functional
independence. The implication of this result is that chaotic motion cannot
exist in these systems. In addition, if the invariant manifold is compact, then
the system is Liouville integrable. As an application, we discuss regimes of
integrability in models of dynamical tunneling and parametric resonance, and in
the dynamics of two-level systems under generic classical fields. A
corresponding quantum algebraic structure is shown to exist which satisfies
analog conditions of Liouville integrability and reproduces the classical
dynamics in an appropriate limit within the Weyl-Wigner formalism. The quantum
analog is then conjectured to be integrable as well.
