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 C1-class diffeomorphism of a closed manifold obeys this closing property on its any hyperbolic invariant subsets.
© de Gruyter 2011