An abstract continuity theorem for Lyapunov exponents of linear cocycles and an application to random cocycles

Pedro Duarte, Silvius Klein

Published 2014-10-02Version 1

We devise an abstract scheme to prove continuity of the Lyapunov exponents for a general class of linear cocycles. The main assumption is a large deviation type (LDT) estimate, uniform in the data. We provide a modulus of continuity that depends explicitly on the sharpness of the LDT estimate. Moreover, we derive such estimates for a class of irreducible random cocycles of Markovian type, thus proving H\"older continuity of their Lyapunov exponents. This is a preliminary version.