Generalized Kolmogorov entropy in the dynamics of multifractal generation

We point out that applying a maximization principle on a Tsallis-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.