scholarly journals Almost Sure Invariance Principle for Nonuniformly Hyperbolic Systems

2005 ◽  
Vol 260 (1) ◽  
pp. 131-146 ◽  
Author(s):  
Ian Melbourne ◽  
Matthew Nicol
2016 ◽  
Vol 16 (03) ◽  
pp. 1660012 ◽  
Author(s):  
Ian Melbourne ◽  
Paulo Varandas

We provide a systematic approach for deducing statistical limit laws via martingale-coboundary decomposition, for nonuniformly hyperbolic systems with slowly contracting and expanding directions. In particular, if the associated return time function is square-integrable, then we obtain the central limit theorem, the weak invariance principle, and an iterated version of the weak invariance principle.


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