Comment on "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 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.