Abstract
There exist special values of a control parameter for which a self-similar hierarchy of islands occurs in the phase space of a system with chaotic dynamics. This set of islands impose an anomalous diffusion of particles which can be described by a fractional kinetic equation with fractional derivatives in space and time. The corresponding exponents of the derivatives can be related to the self-similarity properties of the islands using the renormalization group approach. Examples are given for the web-map and standard map.
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