Uniformly Hyperbolic Finite-Valued SL(2,R)-Cocycles
  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. 
Artur Avila, Jairo Bochi, and Jean-Christophe Yoccoz