3 papers
cond-mat.stat-mech2025
Central Limit Behavior at the Edge of Chaos in the z-Logistic Map
Abbas Ali Saberi, Ugur Tirnakli, Constantino Tsallis
We focus on the FeigenbaumCoulletTresser point of the dissipative one-dimensional z logistic map. We show that sums of iterates converge to q Gaussian distributions, which optimize…
stat.ME2025
Independent Approximates provide a maximum likelihood estimate for heavy-tailed distributions
Amenah AL-Najafi, Ugur Tirnakli, Kenric P. Nelson
Heavy-tailed distributions are infamously difficult to estimate because their moments tend to infinity as the shape of the tail decay increases. Nevertheless, this study shows the…
cond-mat.stat-mech2024
Generalization of the Gauss Map: A jump into chaos with universal features
Christian Beck, Ugur Tirnakli, Constantino Tsallis
The Gauss map (or continued fraction map) is an important dissipative one-dimensional discrete-time dynamical system that exhibits chaotic behaviour and which generates a symbolic…