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Stably weakly shadowing transitive sets and dominated splittings


Author: Dawei Yang
Journal: Proc. Amer. Math. Soc. 139 (2011), 2747-2751
MSC (2010): Primary 37-XX; Secondary 37C05, 37D30
Published electronically: March 24, 2011
MathSciNet review: 2801614
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Abstract: We prove that for any $ C^1$-stably weakly shadowing transitive set $ \Lambda$, either $ \Lambda$ is a sink or a source or $ \Lambda$ admits a dominated splitting.


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Additional Information

Dawei Yang
Affiliation: School of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China
Email: yangdw1981@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10699-3
Received by editor(s): March 10, 2010
Received by editor(s) in revised form: July 12, 2010
Published electronically: March 24, 2011
Communicated by: Yingfei Yi
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.