Temporal scaling at Feigenbaum points and nonextensive thermodynamics.
We show that recent claims for the nonstationary behavior of the logistic map at the Feigenbaum point based on nonextensive thermodynamics are either incorrect 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 attempts at 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 nonextensive thermodynamics.
Grassberger
Peter
P
John-von-Neumann Institute for Computing, Forschungszentrum Jülich, D-52425 Jülich, Germany.