Almost Sure Invariance Principle For Nonuniformly Hyperbolic Systems

Abstract

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.

21 pages, To appear in Communications in Mathematical Physics

References in corpus (1)

• Markov structures and decay of correlations for non-uniformly expanding dynamical systems

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