Regularity and convergence rates for the Lyapunov exponents of linear co-cycles

Abstract

We study linear co-cycles in GL(d,R) (or C) depending on a parameter (in a Lipschitz or Holder fashion) and establish Holder regularity of the Lyapunov exponents for the shift dynamics on the base. We also obtain rates of convergence of the finite volume exponents to their infinite volume limits. The technique is that developed jointly with Michael Goldstein for Schroedinger co-cycles. In particular, we extend the Avalanche Principle, which had been formulated originally for SL(2,R) co-cycles, to GL(d,R).