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The Coupling Method and Exponential Decay of Correlations for The Expanding Maps
WANG Fang
School of Mathematical Sciences, Capital Normal University, Beijing, 100048
*Correspondence author
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Funding: Specialized Research Fund for the Doctoral Program of Higher Education （No.20111108120001）
Opened online:23 December 2014
Accepted by: none
Citation: WANG Fang.The Coupling Method and Exponential Decay of Correlations for The Expanding Maps[OL]. [23 December 2014] http://en.paper.edu.cn/en_releasepaper/content/4623829
 
 
In this article, we consider the standard expanding map $T: mathbb{S}^1 a mathbb{S}^1$ with $T(x)=2xmod 1$. We prove that the correlations of $C^{r}$ observables decay exponentially with the speed $2^{-rn}$, for both $r in (0,1)$ and $rinZ^+$. The main tool we are using in this work is the coupling method. We remark that our result can be easily extended to general expanding map $T(x)=mxmod 1$, $orall min mathbb{Z}^+$.
Keywords:Dynamical systems; expanding map; correlation; coupling method.
 
 
 

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