  In the present paper the Renormalization Group (RG) method is adopted as a
tool for a constructive analysis of the properties of the Frobenius-Perron
Operator. The renormalization group reduction of a generic symplectic map in
the case, where the unperturbed rotation frequency of the map is far from
structural resonances driven by the kick perturbation has been performed in
detail. It is further shown that if the unperturbed rotation frequency is close
to a resonance, the reduced RG map of the Frobenius-Perron operator (or
phase-space density propagator) is equivalent to a discrete Fokker-Planck
equation for the renormalized distribution function. The RG method has been
also applied to study the stochastic properties of the standard Chirikov-Taylor
map.
