1978/01/01 by Uǧur Tırnaklı, Ugur Tirnakli, Monique Brunet-Weinmann
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Archaeology #Art #Artificial intelligence #CHAOS (operating system) #Chaos control and synchronization #Chaotic #Civilization #Complex Systems and Time Series Analysis #Computation #Computer science #Divergence (linguistics) #Edge of chaos #Fractal #History #Hénon map #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Measure (data warehouse) #Mixing (physics) #Multifractal system #Physics #Statistical Mechanics and Entropy #Statistical physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.66.066212
4 pages, 3 figures
openalex publication_date 1978/01/01 · arxiv created 2002/08/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/28
The mixing properties (or sensitivity to initial conditions) of the two-dimensional Henon map have been explored numerically at the edge of chaos. Three independent methods, which have been developed and used so far for one-dimensional maps, have been used to accomplish this task. These methods are (i) the measure of the divergence of initially nearby orbits, (ii) analysis of the multifractal spectrum, and (iii) computation of nonextensive entropy increase rates. The results obtained closely agree with those of the one-dimensional cases and constitute a verification of this scenario in two-dimensional maps. This obviously makes the idea of weak chaos even more robust.