Dissipation time and decay of correlations
Dissipation time and decay of correlations
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耗散时间和相关性衰减
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
L. Wołowski
中科院分区：
文献类型：
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作者：
A. Fannjiang;S. Nonnenmacher;L. Wołowski
我们考虑了噪声对d维环面上保体积映射所产生的动力学的影响。我们用来测量动力学不可逆性的量是耗散时间。在小噪声极限下，我们重点研究了该时间的渐近行为。根据映射及其传播子的各种性质：谱性质、局部可扩性和全局混合性质，我们得到了耗散时间的普遍下界和上界。我们证明了对于一类一般的非弱混合映射，耗散是慢的；另一方面，对于一大类指数混合系统，包括一致扩展映射和Anosov微分同态，它是快的。
We consider the effect of noise on the dynamics generated by volume-preserving maps on a d-dimensional torus. The quantity we use to measure the irreversibility of the dynamics is the dissipation time. We focus on the asymptotic behaviour of this time in the limit of small noise. We derive universal lower and upper bounds for the dissipation time in terms of various properties of the map and its associated propagators: spectral properties, local expansivity, and global mixing properties. We show that the dissipation is slow for a general class of non-weakly-mixing maps; on the other hand, it is fast for a large class of exponentially mixing systems, which include uniformly expanding maps and Anosov diffeomorphisms.