scholarly journals Almost Sure Invariance Principle for Nonuniformly Hyperbolic Systems

2005 ◽  
Vol 260 (1) ◽  
pp. 131-146 ◽  
Author(s):  
Ian Melbourne ◽  
Matthew Nicol
Keyword(s):  
Invariance Principle ◽  
Hyperbolic Systems ◽  
Almost Sure Invariance Principle ◽  
Nonuniformly Hyperbolic

scholarly journals A note on statistical properties for nonuniformly hyperbolic systems with slow contraction and expansion

2016 ◽  
Vol 16 (03) ◽  
pp. 1660012 ◽  
Author(s):  
Ian Melbourne ◽  
Paulo Varandas
Keyword(s):  
Invariance Principle ◽  
Hyperbolic Systems ◽  
Return Time ◽  
Limit Laws ◽  
Weak Invariance Principle ◽  
Weak Invariance ◽  
The Central Limit Theorem ◽  
Statistical Limit ◽  
Contraction And Expansion ◽  
Nonuniformly Hyperbolic

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.

scholarly journals On the uniform hyperbolicity of some nonuniformly hyperbolic systems

2002 ◽  
Vol 131 (4) ◽  
pp. 1303-1309 ◽  
Author(s):  
José F. Alves ◽  
Vítor Araújo ◽  
Benoît Saussol
Keyword(s):  
Hyperbolic Systems ◽  
Uniform Hyperbolicity ◽  
Nonuniformly Hyperbolic
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