## Abstract

Let be a Hölder-continuous linear cocycle with a discrete-time, *μ*-measure-preserving driving flow ƒ: *X* × ℤ → *X* on a compact metric space *X*. We show that the Lyapunov characteristic spectrum of (, *μ*) can be approached arbitrarily by that of periodic points. Consequently, if all periodic points have only nonzero Lyapunov exponents and such exponents are uniformly bounded away from zero, then (, *μ*) also has only non-zero Lyapunov exponents. In our arguments, an exponential closing property of the driving flow is a basic condition. And we prove that every *C*
^{1}-class diffeomorphism of a closed manifold obeys this closing property on its any hyperbolic invariant subsets.

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