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Diffeomorphisms with global dominated splittings cannot be minimal


Author: Pengfei Zhang
Journal: Proc. Amer. Math. Soc. 140 (2012), 589-593
MSC (2010): Primary 37D30
DOI: https://doi.org/10.1090/S0002-9939-2011-10956-0
Published electronically: June 10, 2011
MathSciNet review: 2846327
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ M$ be a closed manifold and $ f$ be a diffeomorphism on $ M$. We show that if $ f$ has a nontrivial dominated splitting $ TM=E\oplus F$, then $ f$ cannot be minimal. The proof mainly uses Mañé's argument and Liao's selecting lemma.


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Additional Information

Pengfei Zhang
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China
Address at time of publication: CEMA, Central University of Finance and Economics, Beijing 100081, People’s Republic of China
Email: pfzh311@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2011-10956-0
Keywords: Dominated splitting, minimal, Liao’s sifting lemma, Liao’s selecting lemma, periodic shadowing.
Received by editor(s): November 24, 2010
Published electronically: June 10, 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.

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