A note on approximation properties of the Oseledets splitting

Liang, Chao; Liao, Gang; Sun, Wenxiang

doi:10.1090/S0002-9939-2014-12093-4

A note on approximation properties of the Oseledets splitting
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by Chao Liang, Gang Liao and Wenxiang Sun PDF

Proc. Amer. Math. Soc. 142 (2014), 3825-3838 Request permission

Abstract:

We prove that the Oseledets splitting, mean angle and independence number of an ergodic hyperbolic measure of a $C^{1+ r}$ diffeomorphism can be approximated by those of atomic measures on hyperbolic periodic orbits. This removes the assumption on simple spectrum in an earlier paper by the authors and strengthens Katok’s closing lemma by presenting more information about not only the state space but also its linearization.

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