Dresden 2003 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 46: Poster

DY 46.20: Poster

Donnerstag, 27. März 2003, 15:30–18:00, P1

Fractality of deterministic diffusion in nonhyperbolic maps — •Nickolay Korabel and Rainer Klages — Max-Planck-Institut für Physik komplexer Systeme, NöthnitzerStraße 38, D-01187 Dresden, Germany

The nonlinear climbing sine map is a nonhyperbolic dynamical system exhibiting both normal and anomalous diffusion under variation of a control parameter. We show that on a suitable coarse scale this map generates an oscillating parameter-dependent diffusion coefficient, similarly to hyperbolic maps, whose asymptotic functional form can be understood in terms of simple random walk approximations. On finer scales we find fractal hierarchies of normal and anomalous diffusive regions as functions of the control parameter [1]. By using a Green-Kubo formula for diffusion the origin of these different regions is systematically traced back to strong dynamical correlations. Starting from the equations of motion of the map these correlations are formulated in terms of fractal generalized Takagi functions obeying generalized de Rham-type functional recursion relations. We analyze the measure of the normal and anomalous diffusive regions in the parameter space showing that in both cases it is positive, and that for normal diffusion it increases by increasing the parameter value [2].

[1] N.Korabel, R.Klages, Phys. Rev. Lett. 89, 214102-1–4 (2002).

[2] N.Korabel, R.Klages, e-print nlin.CD/0211012 (Nov. 2002).