2003/12/29 by Ernesto P. Borges, Uǧur Tırnaklı, Ugur Tirnakli
Economics, Econometrics and Finance · Environmental Science · Physics and Astronomy · #Complex Systems and Time Series Analysis #Ecosystem dynamics and resilience #Statistical Mechanics and Entropy #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.physa.2004.04.011
published as Physica A 340 227--233 (2004) · Communication at NEXT2003, Second Sardinian International Conference on News and Expectations in Thermostatistics, Villasimius (Cagliari) Italy, 21-28 September 2003. Submitted to Physica A. Elsevier Latex, 8 pages, 6 eps figures
arxiv created 2003/12/29 · openalex publication_date 2004/04/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The sensitivity to initial conditions and relaxation dynamics of two-dimensional maps are analyzed at the edge of chaos, along the lines of nonextensive statistical mechanics. We verify the dual nature of the entropic index for the Henon map, one (qsen<1) related to its sensitivity to initial conditions properties, and the other, graining-dependent (qrel(W)>1), related to its relaxation dynamics towards its stationary state attractor. We also corroborate a scaling law between these two indexes, previously found for z-logistic maps. Finally we perform a preliminary analysis of a linearized version of the Henon map (the smoothed Lozi map). We find that the sensitivity properties of all these z-logistic, Henon and Lozi maps are the same, qsen=0.2445...