  We consider linear cocycles over non-uniformly hyperbolic dynamical systems.
The base system is a diffeomorphism $f$ of a compact manifold $X$ preserving a
hyperbolic ergodic probability measure $\mu$. The cocycle $A$ over $f$ is
Holder continuous and takes values in $GL(d,R)$ or, more generally, in the
group of invertible bounded linear operators on a Banach space. For a
$GL(d,R)$-valued cocycle $A$ we prove that the Lyapunov exponents of $A$ with
respect to $\mu$ can be approximated by the Lyapunov exponents of $A$ with
respect to measures on hyperbolic periodic orbits of $f$. In the
infinite-dimensional setting one can define the upper and lower Lyapunov
exponents of $A$ with respect to $\mu$, but they cannot always be approximated
by the exponents of $A$ on periodic orbits. We prove that they can be
approximated in terms of the norms of the return values of $A$ on hyperbolic
periodic orbits of $f$.
