Almost sure invariance principle for nonuniformly hyperbolic systems

被引：121

作者：

Melbourne, I ^{[1
]}

Nicol, M

机构：

[1] Univ Surrey, Dept Math & Stat, Guildford GU2 7XH, Surrey, England

[2] Univ Houston, Dept Math, Houston, TX 77204 USA

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2005年 / 260卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

D O I：

10.1007/s00220-005-1407-5

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We prove an almost sure invariance principle that is valid for general classes of nonuniformly expanding and nonuniformly hyperbolic dynamical systems. Discrete time systems and flows are covered by this result. In particular, the result applies to the planar periodic Lorentz flow with finite horizon. Statistical limit laws such as the central limit theorem, the law of the iterated logarithm, and their functional versions, are immediate consequences.

引用

页码：131 / 146

页数：16

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