Temporal scaling at Feigenbaum points and non-extensive thermodynamics

Details Temporal scaling at Feigenbaum points and non-extensive thermodynamics Temporal scaling at Feigenbaum points and non-extensive thermodynamics

2005-08-03

arxiv.org/abs/cond-mat/0508110v1

Physics

Condensed Matter

Statistical Mechanics

accepted for Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.95.140601

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.

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