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Licensed Unlicensed Requires Authentication Published by De Gruyter April 2, 2011

Exponential closing property and approximation of Lyapunov exponents of linear cocycles

Xiongping Dai
From the journal

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.

Received: 2008-10-09
Revised: 2009-04-25
Published Online: 2011-04-02
Published in Print: 2011-March

© de Gruyter 2011