Long-Time Behavior of Weakly Coupled Oscillators
Long-Time Behavior of Weakly Coupled Oscillators
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DOI：
10.1007/s10955-006-9133-8
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发表时间：
2006-07
影响因子：
1.6
通讯作者：
M. Freidlin;A. Wentzell
中科院分区：
文献类型：
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作者：
M. Freidlin;A. Wentzell
我们考虑一个简单的多自由度完全可积系统的小扰动：一个独立的一自由度振子的集合(在扰动系统中，单个振子不再是独立的)。我们证明了这样一个系统的长期行为，即使在纯确定性扰动的情况下，一般也应该被描述为一个随机过程。极限随机过程是开卷空间上的马尔可夫过程，对应于非扰动系统的第一积分的集合。
We consider small perturbations of a simple completely integrable system with many degrees of freedom: a collection of independent one-degree-of-freedom oscillators (in the perturbed system the individual oscillators are no longer independent). We show that the long-time behavior of such a system, even in the case of purely deterministic perturbations, should, in general, be described as a stochastic process. The limiting stochastic process is a Markov process on an open book space corresponding to the collection of first integrals of the non-perturbed system.