Almost Sure Invariance Principle For Nonuniformly Hyperbolic Systems

Details Almost Sure Invariance Principle For Nonuniformly Hyperbolic Systems Almost Sure Invariance Principle For Nonuniformly Hyperbolic Systems

2005-03-29

arxiv.org/abs/math/0503693v1

Mathematics

Dynamical Systems

21 pages, To appear in Communications in Mathematical Physics

Scientific paper

10.1007/s00220-005-1407-5

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.

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