Comment on "Central limit behavior in deterministic dynamical systems"

TL;DR

This paper critically examines claims of a generalized central limit theorem at the Feigenbaum point in the logistic map, finding inconsistencies with high-statistics simulations and refuting extended claims by the same authors.

Contribution

It provides a rigorous critique of recent claims about generalized CLT behavior at the Feigenbaum point, clarifying the limitations of those assertions.

Findings

No evidence supporting the generalized CLT at the Feigenbaum point

High-statistics simulations contradict the claimed behavior

Refutes extended claims made by the original authors

Abstract

We check claims for a generalized central limit theorem holding at the Feigenbaum (infinite bifurcation) point of the logistic map, made recently by U. Tirnakli, C. Beck, and C. Tsallis (Phys. Rev. {\bf 75}, 040106(R) (2007)). We show that there is no obvious way that these claims can be made consistent with high statistics simulations. We also refute more recent claims by the same authors that extend the claims made in the above reference.