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

Ozgur Afsar; Ugur Tirnakli

doi:10.1209/0295-5075/101/20003

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arXiv · 1211.1838

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

Ozgur Afsar·Ugur Tirnakli

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Abstract

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.

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Ozgur Afsar, Ugur Tirnakli. 2012-11-08. Generalized Huberman-Rudnick scaling law and robustness of $q$-Gaussian probability distributions. https://doi.org/10.1209/0295-5075%2F101%2F20003

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