Phantoms of regularity in the sea of quantum chaos

The concept of the effective quasi-Hamiltonian of a quantum map is proposed. It is shown, using Chirikov's standard map as an example, how such a Hamiltonian is constructed in the form of a power expansion near the points of the quantum resonances. In these points, the evolution is connected to continuous gauge transformations from the unitary unimodular group. Within some domain near a resonance of the order q , the evolution turns out to be equivalent to the regular conservative motion along a circle in a ( q 2 −1)-component inhomogeneous “magnetic” field of a particle with q intrinsic degrees of freedom described by the SU ( q ) group.