Nonextensive Pesin identity: Exact renormalization group analytical results for the dynamics at the edge of chaos of the logistic map

2003/04/30 by Fulvio Baldovin, A. Robledo, Alberto Robledo · 4 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #Statistical Mechanics and Entropy #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.69.045202

published as Phys. Rev. E 69, 045202(R)(2004) · Revtex, 5 pages, 3 figures

openalex publication_date 2004/04/28 · arxiv created 2004/05/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the dynamical and entropic properties at the chaos threshold of the logistic map are naturally linked through the nonextensive expressions for the sensitivity to initial conditions and for the entropy. We corroborate analytically, with the use of the Feigenbaum renormalization group transformation, the equality between the generalized Lyapunov coefficient lambda(q) and the rate of entropy production, K(q), given by the nonextensive statistical mechanics. Our results advocate the validity of the q -generalized Pesin identity at critical points of one-dimensional nonlinear dissipative maps.

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