Uniformity of singular value exponents for typical cocycles

Abstract

Let [Formula: see text] be a [Formula: see text]-valued cocycle over a subshift of finite type. Under a certain twisting assumption, we prove that [Formula: see text] has a uniform Lyapunov exponent if and only if the largest Lyapunov exponent of [Formula: see text] at all periodic points equals. Under the typicality assumption, we give two checkable criteria for deciding whether [Formula: see text] has uniform singular value exponents.