We consider finite families of SL(2,ℝ) matrices whose products display uniform exponential growth. These form open subsets of (SL(2,ℝ))N, and we study their components, boundary, and complement. We also consider the more general situation where the allowed products of matrices satisfy a Markovian rule.
Cite this article
Artur Avila, Jairo Bochi, Jean-Christophe Yoccoz, Uniformly hyperbolic finite-valued SL(2,ℝ)-cocycles. Comment. Math. Helv. 85 (2010), no. 4, pp. 813–884DOI 10.4171/CMH/212