Uniformly Hyperbolic Finite-Valued SL(2,R)-Cocycles

2008/08/01 by Artur Avila, Jairo Bochi, Jean-Christophe Yoccoz · 1 citation
Mathematics · #math.DS

paper · pdf · doi:10.4171/cmh/212

published as Commentarii Mathematici Helvetici, 85, no. 4 (2010), 813-884 · 64 pages, 16 figures

arxiv created 2008/08/01 · arxiv updated 2011/02/25

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.

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