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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stably inverse shadowable transitive sets and dominated splitting


Authors: Keonhee Lee and Manseob Lee
Journal: Proc. Amer. Math. Soc. 140 (2012), 217-226
MSC (2000): Primary 37D30; Secondary 37C50
Published electronically: May 19, 2011
MathSciNet review: 2833534
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Abstract: Let $ f$ be a diffeomorphism of a closed $ n$-dimensional smooth manifold. In this paper, we show that if $ f$ has the $ C^1$-stably inverse shadowing property on a transitive set, then it admits a dominated splitting.


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Additional Information

Keonhee Lee
Affiliation: Department of Mathematics, Chungnam National University, Daejeon, 305-764, Republic of Korea
Email: khlee@cnu.ac.kr

Manseob Lee
Affiliation: Department of Mathematics, Mokwon University, Daejeon, 302-729, Republic of Korea
Email: lmsds@mokwon.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10882-7
PII: S 0002-9939(2011)10882-7
Keywords: Dominated splitting, genericity, inverse shadowing, transitive set.
Received by editor(s): June 15, 2010
Received by editor(s) in revised form: October 7, 2010, and November 3, 2010
Published electronically: May 19, 2011
Additional Notes: The second author is the corresponding author.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.