Probability densities for the sums of iterates of the sine-circle map in the vicinity of the quasiperiodic edge of chaos
Articles > Article · 2010
Authors: Özgür AFŞAR, Uğur TIRNAKLI
Physical Review E, Journal Indexed in SCI Expanded, International, WoS, 2010, vol 82, pp 046210-046210
DOI: 10.1103/physreve.82.046210
Summary
We investigate the probability density of rescaled sum of iterates of sine-circle map within quasiperiodic route to chaos. When the dynamical system is strongly mixing (i.e., ergodic), standard central limit theorem (CLT) is expected to be valid, but at the edge of chaos where iterates have strong correlations, the standard CLT is not necessarily valid anymore. We discuss here the main characteristics of the probability densities for the sums of iterates of deterministic dynamical systems which exhibit quasiperiodic route to chaos. At the golden-mean onset of chaos for the sine-circle map, we numerically verify that the probability density appears to converge to a q-Gaussian with q<1 as the golden mean value is approached.