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

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.
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2009
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Artur Avila, Thomas Roblin. Uniform exponential growth for some SL(2,R) matrix products. 2009. 〈hal-00365299〉

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