Periodic approximation of exceptional lyapunov exponents for semi-invertible operator cocycles

Abstract

We prove that for semi-invertible and Hölder continuous linear cocycles A acting on an arbitrary Banach space and defined over a base space that satisfies the Anosov closing property, all exceptional Lyapunov exponents of A with respect to an ergodic invariant measure for base dynamics can be approximated with Lyapunov exponents of A with respect to ergodic measures supported on periodic orbits. Our result is applicable to a wide class of infinite-dimensional dynamical systems.