Abstract
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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
