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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Diffeomorphisms with global dominated splittings cannot be minimal
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by Pengfei Zhang PDF
Proc. Amer. Math. Soc. 140 (2012), 589-593 Request permission

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
  • Received by editor(s): November 24, 2010
  • Published electronically: June 10, 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. 140 (2012), 589-593
  • MSC (2010): Primary 37D30
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10956-0
  • MathSciNet review: 2846327