Comment on "Analysis of chaotic motion and its shape dependence in a generalized piecewise linear map".
Rajagopalan and Sabir [Phys. Rev. E 63, 057201 (2001)] recently discussed deterministic diffusion in a piecewise linear map using an approach developed by Fujisaka et al. We first show that they rederived the random walk formula for the diffusion coefficient, which is known to be the exact result for maps of Bernoulli-type since the work of Fujisaka and Grossmann [Z. Phys. B: Condens. Matter 48, 261 (1982)]. However, this correct solution is at variance to the diffusion coefficient curve presented in their paper. Referring to another existing approach based on Markov partitions, we answer the question posed by the authors regarding solutions for more general parameter values by recalling the finding of a fractal diffusion coefficient. We finally argue that their model is not suitable for studying intermittent behavior, in contrast to what was suggested in their paper.
Klages
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Max Planck Institute for Physics of Complex Systems, Nöthnitzer Strasse 38, D-01187 Dresden, Germany. rklages@mpipks-dresden.mpg.de