  We present a kicked harmonic oscillator where the impulsive driving is
provided by stroboscopic measurements on an ancillary degree of freedom and not
by the canonical quantization of a time-dependent Hamiltonian. The ancila is
dynamically entangled with the oscillator position, while the background
Hamiltonian remains static. The dynamics of this system is determined in closed
analytical form, allowing for the evaluation of a properly defined Loschmidt
echo, ensemble averages, and phase-space portraits. As in the case of standard
Floquet systems we observe regimes with crystalline and quasicrystalline
structures in phase space, resonances, and evidences of chaotic behavior,
however, not originating from any classically chaotic system.
