Quasiscalar map for a kicked spin 1/2

We study the semiclassical dynamics of a spin 1/2 system polarized in an external magnetic field, coupled to a dissipative heat reservoir and periodically perturbed by an instantaneous rotation. We construct a quasiscalar map for a dynamical invariant of the unperturbed system and investigate its characteristics for both the Rotating Wave Approximation and the Full Coupling descriptions of the dissipative environment in terms of the kicking strength and the orientation of the rotation axis.