  The correspondence principle plays an important role in understanding the
emergence of classical chaos from an underlying quantum mechanics. Here we
present an infinite family of quantum dynamics that never resembles the
analogous classical chaotic dynamics irrespective of dimension. These take the
form of stroboscopic unitary evolutions in the quantum kicked top that act as
the identity after a finite number of kicks. Because these state-independent
temporal periodicities are present in all dimensions, their existence
represents a universal violation of the correspondence principle. We further
discuss the relationship of these periodicities with the quantum kicked rotor,
in particular the phenomenon of quantum anti-resonance.

Quantum Physics;Chaotic Dynamics