On the multifractal nature of fully developed turbulence and chaotic systems

It is generally argued that the energy dissipation of three-dimensional turbulent flow is concentrated on a set with non-integer Hausdorff dimension. Recently, in order to explain experimental data, it has been proposed that this set does not possess a global dilatation invariance: it can be considered to be a multifractal set. In this paper a review is conducted of the concept of multifractal sets in both turbulent flows and dynamical systems using a generalization of the beta-model.