正弦-圆映射在拟周期混沌边缘附近迭代和的概率密度
Probability densities for the sums of iterates of the sine-circle map in the vicinity of the quasi-periodic edge of chaos
摘要：
研究了正弦-圆映射重标迭代和在拟周期路径下的概率密度。当动力系统是强混合时（即，遍历），标准的中心极限定理（CLT）被期望是有效的，但在迭代具有强相关性的混沌边缘，标准的CLT不一定再有效。本文讨论了具有拟周期性混沌路径的确定性动力系统的中心极限行为的主要特征。在正弦圆映射的金均值混沌开始时，我们数值验证了概率密度似乎收敛到一个q-高斯与q<1的黄金均值接近。
英文摘要：
We investigate the probability density of rescaled sum of iterates of sine-circle map within quasi-periodic 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 to be valid anymore. We discuss here the main characteristics of the central limit behavior of deterministic dynamical systems which exhibit quasi-periodic 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.
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