# American Institute of Mathematical Sciences

October  2009, 3(4): 549-554. doi: 10.3934/jmd.2009.3.549

## Uniform exponential growth for some SL(2, R) matrix products

 1 CNRSUMR 7599, Laboratoire de Probabilités et Modèles aléatoires, Université Pierre et Marie Curie–Boîte courrier 188, 75252–Paris Cedex 05, France 2 CNRS UMR 7599, Laboratoire de Probabilités et Modèles aléatoires, Université Pierre et Marie Curie–Boîte courrier 188. 75252–Paris Cedex 05, France

Received  April 2009 Revised  September 2009 Published  January 2010

Given a hyperbolic matrix $H\in SL(2,\R)$, we prove that for almost every $R\in SL(2,\R)$, any product of length $n$ of $H$ and $R$ grows exponentially fast with $n$ provided the matrix $R$ occurs less than $o(\frac{n}{\log n\log\log n})$ times.
Citation: Artur Avila, Thomas Roblin. Uniform exponential growth for some SL(2, R) matrix products. Journal of Modern Dynamics, 2009, 3 (4) : 549-554. doi: 10.3934/jmd.2009.3.549
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