Proposed central limit behavior in deterministic dynamical systems.
We check claims for a generalized central limit theorem holding at the Feigenbaum (infinite bifurcation) point of the logistic map made recently by Tirnakli, Phys. Rev. 75, 040106(R) (2007); this issue, Phys. Rev.79, 056209 (2009). We show that there is no obvious way that these claims can be made consistent with high statistics simulations. Instead, we find other scaling laws for related quantities.
Grassberger
Peter
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Department of Physics and Astronomy, Complexity Science Group, University of Calgary, Calgary, Alberta, Canada T2N 1N4.