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Journal of Modern Dynamics (JMD)
 

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

Pages: 549 - 554, Issue 4, October 2009      doi:10.3934/jmd.2009.3.549

 
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Artur Avila - CNRSUMR 7599, Laboratoire de Probabilités et Modèles aléatoires, Université Pierre et Marie Curie–Boîte courrier 188, 75252–Paris Cedex 05, France (email)
Thomas Roblin - CNRS UMR 7599, Laboratoire de Probabilités et Modèles aléatoires, Université Pierre et Marie Curie–Boîte courrier 188. 75252–Paris Cedex 05, France (email)

Abstract: 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.

Keywords:   SL(2, R), matrix products, hyperbolicity, Lyapounov exponent.
Mathematics Subject Classification:   Primary: 37H15; Secondary: 37C85.

Received: April 2009;      Revised: September 2009;      Available Online: January 2010.