Multifractal approach to fully developed turbulence

The multifractal description of complex phenomena has been introduced in the first half of the 1980s for the characterization of the anomalous scaling of the fully developed turbulence and the structure of the chaotic attractors. From a technical point of view, the idea of the multifractal is basically contained in the large deviations theory; however, the introduction of the multifractal description in 1980s had an important role in statistical physics, chaos, and disordered systems. In particular, to clarify in a neat way that the usual idea, coming from critical phenomena, that just few scaling exponents are relevant, cannot be completely accurate, and an infinite set of exponents is necessary for a complete characterization of the scaling features. We briefly review here the basic aspects and some applications of the multifractal model for turbulence.