title: Fractal properties of anomalous diffusion in intermittent maps.
abstract: An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous time random-walk theory well approximates the coarse behavior of this quantity in terms of a continuous function. This theory also reproduces a full suppression of the strength of diffusion, which occurs at the dynamical transition from normal to anomalous diffusion. Similarly, the probability density function of this map exhibits a nontrivial fine structure while its coarse functional form is governed by a time fractional diffusion equation. A more detailed understanding of the irregular structure of the generalized diffusion coefficient is provided by an anomalous Taylor-Green-Kubo formula establishing a relation to de Rham-type fractal functions.
authors.affiliation: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012, USA.
authors.forename: Nickolay
authors.initials: N
authors.lastname: Korabel
authors.forename: Rainer
authors.initials: R
authors.lastname: Klages
authors.forename: Aleksei V
authors.initials: AV
authors.lastname: Chechkin
authors.forename: Igor M
authors.initials: IM
authors.lastname: Sokolov
authors.forename: Vsevolod Yu
authors.initials: VY
authors.lastname: Gonchar