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We investigate the probability density of rescaled sum of iterates ofsine-circle map within quasi-periodic route to chaos. When the dynamical systemis strongly mixing (i.e., ergodic), standard Central Limit Theorem (CLT) isexpected to be valid, but at the edge of chaos where iterates have strongcorrelations, the standard CLT is not necessarily to be valid anymore. Wediscuss here the main characteristics of the central limit behavior ofdeterministic dynamical systems which exhibit quasi-periodic route to chaos. Atthe golden-mean onset of chaos for the sine-circle map, we numerically verifythat the probability density appears to converge to a q-Gaussian with q<1 asthe golden mean value is approached.

Probability densities for the sums of iterates of the sine-circle map in the vicinity of the quasi-periodic edge of chaos