Lyapunov exponents of analytic cocycles with singularities

Pedro Duarte, Silvius Klein

Published 2014-10-03Version 1

Consider the space of quasiperiodic, higher dimensional linear cocycles. Assuming the base dynamics fixed and defined by a Diophantine torus translation, and the fibre action depending analytically on the base point and not identically singular, we prove large deviation type estimates for the cocycle. These estimates are stable under small perturbations, which implies, due to a general criterion, that all Lyapunov exponents are continuous everywhere as functions of the cocycle. It also shows that locally, simple Lyapunov exponents are log-H\"older. The main new feature of this paper is allowing a cocycle depending on several variables to have singularities, which requires a careful analysis involving pluri-subharmonic and analytic functions of several variables.