Two inverse problems induced by multifractal phenomena

In frame of the phenomena revealing multifractality, two inverse problems are formulated and their solution is outlined; namley, (i) to what extent the indices characterizing scaling properties of dynamical fluctuations (specified by factorial moments) are determined by means of power law indicesτ(q) which characterize scaling properties of the associated frequency moments, the later moments representing asymptotics (for sufficiently large multiplicities) of the former ones, and (ii) to what extent the scaling indicesτ(q) are determined by their asymptotic properties (at large absolute value of the orderq ascribed to the associated frequency moments and taken at a finite and fixed energy).