Commentarii Mathematici Helvetici

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Volume 85, Issue 4, 2010, pp. 813–884
DOI: 10.4171/CMH/212

Published online: 2010-08-31

Uniformly hyperbolic finite-valued SL(2,ℝ)-cocycles

Artur Avila[1], Jairo Bochi[2] and Jean-Christophe Yoccoz[3]

(1) Université Pierre et Marie Curie, Paris, France
(2) PUC-Rio, Rio de Janeiro, Brazil
(3) Collège de France, Paris, France

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.

Keywords: Linear cocycles, uniform hyperbolicity, bifurcations, iterated function systems

Avila Artur, Bochi Jairo, Yoccoz Jean-Christophe: Uniformly hyperbolic finite-valued SL(2,ℝ)-cocycles. Comment. Math. Helv. 85 (2010), 813-884. doi: 10.4171/CMH/212