Generalized Huberman-Rudnick scaling law and robustness of q-Gaussian probability distributions
1 Department of Physics, Faculty of Science, Ege University - 35100 Izmir, Turkey
2 Division of Statistical Mechanics and Complexity, Institute of Theoretical and Applied Physics (ITAP) Kaygiseki Mevkii - 48740 Turunc, Mugla, Turkey
Received: 16 November 2012
Accepted: 2 January 2013
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.
PACS: 05.45.Ac – Low-dimensional chaos / 05.20.-y – Classical statistical mechanics / 05.45.Pq – Numerical simulations of chaotic systems
© EPLA, 2013