Commentarii Mathematici Helvetici
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Uniformly hyperbolic finite-valued SL(2,ℝ)-cocyclesArtur Avila, Jairo Bochi and Jean-Christophe Yoccoz (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