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

Artur Avila (1, 2) , Thomas Roblin (2)

1 IMPA Jean-Christophe Yoccoz
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Domaines: Mathématiques générales [math.GM]

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