  The quantum kicked rotor (QKR) 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 {\it
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 non-linear resonance.
