  We show that recent claims for the non-stationary behaviour of the logistic
map at the Feigenbaum point based on non-extensive thermodynamics are either
wrong or can be easily deduced from well-known properties of the Feigenbaum
attractor. In particular, there is no generalized Pesin identity for this
system, the existing "proofs" being based on misconceptions about basic notions
of ergodic theory. In deriving several new scaling laws of the Feigenbaum
attractor, thorough use is made of its detailed structure, but there is no
obvious connection to non-extensive thermodynamics.
