Generalized Kolmogorov entropy in the dynamics of multifractal generation

We point out that applying a maximization principle on a T sallis-like generalized form of the Kolmogorov entropy for iterated function systems, naturally provides a canonical statistical frame for the description of the multifractal measures generated by such dynamical processes. Multifractal spectra can then be characterized by usual statistical parameters - in particular, the ''temperature''. We show that in the limit of zero ''temperature'' the multifractal measure collapses to a homogeneous distribution over a fractal support. For finite ''temperatures'', multifractal spectra are studied numerically in an illustrative example.