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

Artur Avila, Jairo Bochi, Jean Christophe Yoccoz

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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.

Original languageEnglish (US)
Pages (from-to)813-884
Number of pages72
JournalCommentarii Mathematici Helvetici
Volume85
Issue number4
DOIs
StatePublished - 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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