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Non-zero Lyapunov exponents for some conservative partially hyperbolic systems


Author: Yunhua Zhou
Journal: Proc. Amer. Math. Soc. 143 (2015), 3147-3153
MSC (2010): Primary 37D25; Secondary 37D30
Published electronically: February 17, 2015
MathSciNet review: 3336638
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Abstract: Let $ \text {PH}^{1}_\mu (M,3)$ be the set of $ C^{1}$ conservative partially hyperbolic diffeomorphisms with center dimensions three or less. We prove that there is a dense subset $ \mathcal {H}\subset$$ \text {PH}^{1}_\mu (M,3)$ such that each $ f\in \mathcal {H}$ has non-zero Lyapunov exponents on a set of positive volume.


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Additional Information

Yunhua Zhou
Affiliation: College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, People’s Republic of China
Email: zhouyh@cqu.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-2015-12498-7
Keywords: Lyapunov exponents, partial hyperbolicity, domination
Received by editor(s): December 29, 2011
Received by editor(s) in revised form: March 15, 2014
Published electronically: February 17, 2015
Additional Notes: The author was supported by NSFC (11471056), Natural Science Foundation Project of CQCSTC (cstcjjA00003) and Fundamental Research Funds for the Central Universities (CQDXWL2012008).
Communicated by: Yingfei Yi
Article copyright: © Copyright 2015 American Mathematical Society