Poincaré recurrence:. old and new
Poincaré recurrence:. old and new
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庞加莱递归：新旧。
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
L. Barreira
中科院分区：
文献类型：
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作者：
L. Barreira
庞加莱关于递归的经典定理只给出定性性质的信息。另一方面，关于递归的定量行为所知较少，这显然是一个内在困难而不是缺乏兴趣的问题。在这里，我们讨论了最近的事态发展，包括几乎无处不在的重合的复发率和逐点维数的情况下，双曲动力学。我们还讨论了递归的概积结构，它与稳定流形族和不稳定流形族的乘积结构以及双曲测度的概积结构密切相似.
The classical theorem of Poincaré on recurrence only gives information of qualitative nature. On the other hand it is clearly a matter of intrinsic difficulty and not of lack of interest that less is known concerning the quantitative behavior of recurrence. Here we discuss recent developments that include the almost everywhere coincidence between the recurrence rate and the pointwise dimension in the case of hyperbolic dynamics. We also discuss the almost product structure of recurrence, which closely imitates the product structure provided by the families of stable and unstable manifolds as well as the almost product structure of hyperbolic measures.