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The Hausdorff dimension estimation for an ergodic hyperbolic measure of $ C^1$-diffeomorphism


Authors: Juan Wang and Yongluo Cao
Journal: Proc. Amer. Math. Soc. 144 (2016), 119-128
MSC (2010): Primary 37A05; Secondary 37D25, 37D30
DOI: https://doi.org/10.1090/proc/12696
Published electronically: April 16, 2015
MathSciNet review: 3415582
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Abstract: This paper provides the Hausdorff dimension estimation for an ergodic hyperbolic measure of $ C^1$-diffeomorphism on an $ m$-dimensional compact Riemannian manifold with the assumption that its Oseledet's splitting is a dominated splitting.


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Additional Information

Juan Wang
Affiliation: Department of Mathematics, Soochow University, Suzhou 215006, Jiangsu, People’s Republic of China – and – Department of Mathematics, Suzhou University of Science and Technology, Suzhou 215009, Jiangsu, People’s Republic of China
Email: wangjuan@mail.usts.edu.cn

Yongluo Cao
Affiliation: Department of Mathematics, Soochow University, Suzhou 215006, Jiangsu, People’s Republic of China
Email: ylcao@suda.edu.cn

DOI: https://doi.org/10.1090/proc/12696
Keywords: Dimension, entropy, Lyapunov exponents, dominated splitting
Received by editor(s): August 8, 2014
Received by editor(s) in revised form: November 12, 2014
Published electronically: April 16, 2015
Communicated by: Yingfei Yi
Article copyright: © Copyright 2015 American Mathematical Society

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