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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