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

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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...