Renormalization and central limit theorem for critical dynamical systems with weak external random noise
Renormalization and central limit theorem for critical dynamical systems with weak external random noise
复制标题
具有弱外部随机噪声的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：
2007
期刊：
影响因子：
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通讯作者：
Oliver Rodolfo
中科院分区：
文献类型：
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作者：
Diaz Espinosa;Oliver Rodolfo
研究了弱噪声对临界噪声的影响
We study 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 noise 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 periods. 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.