1211.1838 (Ozgur Afsar et al.)

Generalized Huberman-Rudnick scaling law and robustness of $q$-Gaussian
probability distributions    [PDF]

Ozgur Afsar, Ugur Tirnakli

We generalize Huberman-Rudnick universal scaling law for all periodic windows of the logistic map and show the robustness of $q$-Gaussian probability distributions in the vicinity of chaos threshold. Our scaling relation is universal for the self-similar windows of the map which exhibit period-doubling subharmonic bifurcations. Using this generalized scaling argument, for all periodic windows, as chaos threshold is approached, a developing convergence to $q$-Gaussian is numerically obtained both in the central regions and tails of the probability distributions of sums of iterates.

View original: http://arxiv.org/abs/1211.1838