  We present an effective Hamiltonian theory available for some
quasi-periodically driven quantum systems which does not need the knowledge of
the Fourier frequencies of the control signal. It could also be available for
some chaotically driven quantum systems. It is based on the Koopman approach
which generalizes the Floquet approach used with periodically driven systems.
We show the properties of the quasi-energy states (eigenvectors of the
effective Hamiltonian) as quasi-recurrent states of the quantum system.
