Quasiperiodic 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 quasiperiodic 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 quasiperiodically kicked oscillator moreover is dominated by quasiperiodic analogues of the Floquet theorem. 
Peter Kramer, Tobias Kramer, and Vladimir I. Man'ko