Nonextensivity at the edge of chaos of a new universality class of one-dimensional unimodal dissipative maps
arXiv:0901.4292 · doi:10.1140/epjb/e2009-00054-2
Abstract
We introduce a new universality class of one-dimensional unimodal dissipative maps. The new family, from now on referred to as the ()-{\it logarithmic map}, corresponds to a generalization of the -logistic map. The Feigenbaum-like constants of these maps are determined. It has been recently shown that the probability density of sums of iterates at the edge of chaos of the -logistic map is numerically consistent with a -Gaussian, the distribution which, under appropriate constraints, optimizes the nonadditive entropy . We focus here on the presently generalized maps to check whether they constitute a new universality class with regard to -Gaussian attractor distributions. We also study the generalized -entropy production per unit time on the new unimodal dissipative maps, both for strong and weak chaotic cases. The -sensitivity indices are obtained as well. Our results are, like those for the -logistic maps, numerically compatible with the -generalization of a Pesin-like identity for ensemble averages.
17 pages, 10 figures. To appear in European Physical Journal B