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Two-dimensional dissipative maps at chaos threshold: Sensitivity to initial conditions and relaxation dynamics

Ernesto P. Borges·Ugur Tirnakli
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Abstract

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 ($q_{sen}<1$) related to its sensitivity to initial conditions properties, and the other, graining-dependent ($q_{rel}(W)>1$), 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, $q_{sen}=0.2445...$

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Ernesto P. Borges, Ugur Tirnakli. 2003-12-29. Two-dimensional dissipative maps at chaos threshold: Sensitivity to initial conditions and relaxation dynamics. https://doi.org/10.1016/j.physa.2004.04.011

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