Mixing properties and statistical limit theorems for singular hyperbolic flows without a smooth stable foliation
Mixing properties and statistical limit theorems for singular hyperbolic flows without a smooth stable foliation
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无光滑稳定叶状结构的奇异双曲流的混合特性和统计极限定理
DOI：
10.1016/j.aim.2019.04.007
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发表时间：
2017
影响因子：
1.7
通讯作者：
I. Melbourne
中科院分区：
文献类型：
--
作者：
V. Araújo;I. Melbourne
在过去的10年左右，先进的统计特性，包括指数衰减的相关性，已经建立了某些类别的奇异双曲流在三维。结果特别适用于经典的洛伦兹吸引子。然而，许多证明严重依赖于流的稳定叶理的光滑性，在本文中，我们证明了许多统计性质的奇异双曲流没有光滑性假设的稳定叶理。这些性质包括SRB测度的存在性，中心极限定理和相关的不变性原理，以及混合和混合率的结果。这些性质同样适用于高维奇异双曲流，只要中心不稳定子空间是二维的。
Over the last 10 years or so, advanced statistical properties, including exponential decay of correlations, have been established for certain classes of singular hyperbolic flows in three dimensions. The results apply in particular to the classical Lorenz attractor. However, many of the proofs rely heavily on the smoothness of the stable foliation for the flow.In this paper, we show that many statistical properties hold for singular hyperbolic flows with no smoothness assumption on the stable foliation. These properties include existence of SRB measures, central limit theorems and associated invariance principles, as well as results on mixing and rates of mixing. The properties hold equally for singular hyperbolic flows in higher dimensions provided the center-unstable subspaces are two-dimensional.
影响因子：
2.3
作者：
Melbourne, Ian;Nicol, Matthew
通讯作者：
Nicol, Matthew
影响因子：
1.8
作者：
I. Melbourne
通讯作者：
I. Melbourne
对称系统的中心极限定理和反常扩散的抑制
影响因子：
1.7
作者：
Gottwald G
通讯作者：
Gottwald G