Coexistence of measures with simple Lyapunov spectrum for fiber-bunched cocycles

Abstract

We prove that if a Hölder continuous fiber-bunched cocycle $\hat{A}$ over an invertible hyperbolic transitive shift $\hat{\Sigma }$ satisfies an appropriate strong irreducibility condition on Grassmannians, then $\hat{\Sigma }$ admits an ergodic measure $\hat{\mu }$ with full support and product structure with simple Lyapunov spectrum if and only if any other ergodic measure with full support and product structure also has simple Lyapunov spectrum.

31 pages, 1 figure; comments are welcome