ar X iv : m at h - ph / 0 40 40 06 v 3 1 7 Fe b 20 05 Pure point spectrum for the time - evolution of a periodically rank - N kicked Hamiltonian

We find the conditions under which the spectrum of the unitary timeevolution operator for a periodically rank-N kicked system remains pure point. This stability result allows one to analyse the onset of, or lack of chaos in this class of quantum mechanical systems, extending the results for rank-1 systems produced by Combescure and others. This work includes a number of unitary theorems equivalent to those well known and used in the self-adjoint theory.