Exponential growth of product of matrices in {\rm SL}(2,{\mathbb{R}})

Abstract

In this paper we investigate the exponential growth of products of two matrices . We prove, assuming A is a fixed hyperbolic matrix, that for Lebesgue almost every B, products of length n involving less than nα, 0 ⩽ α < 1/2 matrices B are uniformly bounded from below by γn for some γ > 1.