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 Hami ltonian is constructed in the form of a power expansion near the points of the quantum resonances. In these points, the evolution is connected to cont inuous gauge transformations from the unitary unimodular group. Within some domain near a resonance of the order q. the evolution turns out to be equi valent to the regular conservative motion along a circle in a (q(2) - 1)-co mponent inhomogeneous "magnetic" field of a particle with q intrinsic degre es of freedom described by the SU(q) group. (C) 2001 Elsevier Science B.V. All rights reserved.