Quantum resonances of the kicked rotor and the SU(q) group

The quantum kicked rotor map is embedded into a continuous unitary transformation generated by a time-independent quasi Hamiltonian. In some vicinity of a quantum resonance of order q, we relate the problem to the regular motion along a circle in a (q(2) - 1) component inhomogeneous magnetic field of a quantum particle with q intrinsic degrees of freedom described by the SU(q) group. This motion is in parallel with the classical phase oscillations near a nonlinear resonance.