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A note on approximation properties of the Oseledets splitting


Authors: Chao Liang, Gang Liao and Wenxiang Sun
Journal: Proc. Amer. Math. Soc. 142 (2014), 3825-3838
MSC (2010): Primary 37D05, 37D25, 37C25
DOI: https://doi.org/10.1090/S0002-9939-2014-12093-4
Published electronically: July 2, 2014
MathSciNet review: 3251723
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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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Additional Information

Chao Liang
Affiliation: School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081, People’s Republic of China
Email: chaol@cufe.edu.cn

Gang Liao
Affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
Email: liaogang@math.pku.edu.cn

Wenxiang Sun
Affiliation: LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
Email: sunwx@math.pku.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-2014-12093-4
Keywords: Oseledets splitting, mean angle, independence number
Received by editor(s): May 12, 2012
Received by editor(s) in revised form: November 1, 2012, and November 12, 2012
Published electronically: July 2, 2014
Additional Notes: The first author was supported by NSFC (#10901167), Beijing Higher Education Young Elite Teacher Project, and Program for Innovation Research in Central University of Finance and Economics
The third author was supported by NSFC (#11231001) and Doctoral Education Foundation of China
Communicated by: Yingfei Yi
Article copyright: © Copyright 2014 American Mathematical Society

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