Renormalization and Central Limit Theorem for Critical Dynamical Systems with Weak External Noise
Renormalization and Central Limit Theorem for Critical Dynamical Systems with Weak External Noise
复制标题
弱外噪声临界动力系统的重整化和中心极限定理
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
R. Llave
中科院分区：
文献类型：
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作者：
Oliver Diaz;R. Llave
我们研究了弱噪声对临界一维图的影响；也就是说，具有重正化理论的映射。
我们建立了弱噪声的一维中心极限定理，并获得了收敛速度的 Berry--Esseen 估计。
我们详细分析了周期倍增图和具有黄金平均旋转数的临界圆图的累积图。使用重正化群方法，我们推导出长时间后有效噪声的几个特征的缩放关系。我们使用这些标度关系来表明弱噪声的中心极限定理在两个例子中都成立。
我们注意到，对于此处呈现的结果，地图具有抛物线行为至关重要。对于双曲轨道它们是错误的。
We study of the effect of weak noise on critical one dimensional maps; that is, maps with a renormalization theory.
We establish a one dimensional central limit theorem for weak noises and obtain Berry--Esseen estimates for the rate of this convergence.
We analyze in detail maps at the accumulation of period doubling and critical circle maps with golden mean rotation number. Using renormalization group methods, we derive scaling relations for several features of the effective noise after long times. We use these scaling relations to show that the central limit theorem for weak noise holds in both examples.
We note that, for the results presented here, it is essential that the maps have parabolic behavior. They are false for hyperbolic orbits.