Quasi-periodic propagation in time of some classical/quantum systems: Nielsen's conserved quantity and Floquet properties

We consider classical and quantum propagators for two different time intervals. If these propagators follow one another in a Fibonacci sequence we get a discrete quasi-periodic system. A theorem due to Nielsen provides a novel conserved quantity for this system. The Nielsen quantity controls the transition between commutative and non-commutative propagation in time. The quasi-periodically kicked oscillator, moreover, is dominated by quasi-periodic analogues of the Floquet theorem.