JournalscmhVol. 85, No. 4pp. 813–884

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

  • Artur Avila

    Université Pierre et Marie Curie, Paris, France

  • Jairo Bochi

    PUC-Rio, Rio de Janeiro, Brazil

  • Jean-Christophe Yoccoz

    Collège de France, Paris, France
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Abstract

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. 813–884

DOI 10.4171/CMH/212