Multifractional kinetics

Multifractional generalizations are considered for kinetic description of chaotic dynamics. The multiplicity of dimensions is motivated by the multiplicity of sticky island hierarchies in phase space. The set of such islands is considered as a singular support that, in the large time asymptotics, defines the main features of the kinetics which we call “multifractional”. Finally, the moments of the displacement in phase space are not definied by the only transport exponent. Full transport asymptotically exhibits anomalous diffusion with log-periodic oscillations and with intermittent dependence of the transport exponent and period of oscillations on the order of the considered moment. We speculate on the appearance of the same features in experiments and simulations for particle dispersion in turbulent flows.