Lyapunov irregular set of Banach cocycles

Abstract

Let be a topologically mixing subshift of finite type and let be a Hölder continuous map where is the set of invertible elements of a Banach ring B. We prove that either all ergodic measures have the same maximal Lyapunov exponent, or the irregular set is residual in and has full upper capacity topological entropy of . We also prove for generic fiber-bunched cocycles, similar statements can be strengthened by considering the Bowen topological entropy.