Statistical physics of intermittency: Phase transitions and fluctuations of scaling indices

We propose a new statistical-mechanical formalism to extract the multifractal structure from intermittent phenomena. A simple stochastic model reproducing universal properties of intermittency is solved rigorously, and phase transitions associated with the spectrum of the generalized entropies are studied. We also apply the formalism to the logistic map near the critical point for a period-three cycle. The results are in good agreement with numerical results.