# 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.
Document type :
Preprints, Working Papers, ...
2009

https://hal.archives-ouvertes.fr/hal-00365299
Contributor : Thomas Roblin <>
Submitted on : Monday, March 2, 2009 - 9:47:23 PM
Last modification on : Wednesday, October 12, 2016 - 1:03:37 AM
Document(s) archivé(s) le : Friday, October 12, 2012 - 12:46:54 PM

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mat3.pdf
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### Identifiers

• HAL Id : hal-00365299, version 1

### Citation

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

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