Stably weakly shadowing transitive sets and dominated splittings
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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.References
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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
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2747-2751
- MSC (2010): Primary 37-XX; Secondary 37C05, 37D30
- DOI: https://doi.org/10.1090/S0002-9939-2011-10699-3
- MathSciNet review: 2801614