Communications in Mathematical Physics

, Volume 260, Issue 1, pp 131–146 | Cite as

Almost Sure Invariance Principle for Nonuniformly Hyperbolic Systems

  • Ian Melbourne
  • Matthew Nicol


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.


Neural Network Discrete Time Limit Theorem Statistical Limit General Classis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ian Melbourne
    • 1
  • Matthew Nicol
    • 2
  1. 1.Department of Maths. and Stats.University of SurreyGuildfordUK
  2. 2.Department of Math.University of HoustonHoustonUSA

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