We introduce a new universality class of one-dimensional unimodal dissipative maps. The new family, from now on referred to as the (z1, z2)-logarithmic map,
corresponds to a generalization of the z-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 z-logistic map is numerically consistent with a q-Gaussian, the distribution which, under appropriate constraints, optimizes the nonadditive entropy Sq. We focus here on the presently generalized maps to check whether they constitute a new universality class with regard to q-Gaussian attractor distributions.
We also study the generalized q-entropy production per unit time on the new unimodal dissipative maps, both for strong
and weak
chaotic cases. The q-sensitivity indices are obtained as well.
Our results are, like those for the z-logistic maps, numerically compatible with the q-generalization of a Pesin-like identity for ensemble averages.