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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Quasi-stability of partially hyperbolic diffeomorphisms
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by Huyi Hu and Yujun Zhu PDF
Trans. Amer. Math. Soc. 366 (2014), 3787-3804 Request permission

Abstract:

A partially hyperbolic diffeomorphism $f$ is structurally quasi- stable if for any diffeomorphism $g$ $C^1$-close to $f$, there is a homeomorphism $\pi$ of $M$ such that $\pi \circ g$ and $f\circ \pi$ differ only by a motion $\tau$ along center directions. $f$ is topologically quasi-stable if for any homeomorphism $g$ $C^0$-close to $f$, the above holds for a continuous map $\pi$ instead of a homeomorphism. We show that any partially hyperbolic diffeomorphism $f$ is topologically quasi-stable, and if $f$ has $C^1$ center foliation $W^c_f$, then $f$ is structurally quasi-stable. As applications we obtain continuity of topological entropy for certain partially hyperbolic diffeomorphisms with one or two dimensional center foliation.
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Additional Information
  • Huyi Hu
  • Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
  • Email: hhu@math.msu.edu
  • Yujun Zhu
  • Affiliation: College of Mathematics and Information Science, and Hebei Key Laboratory of Computational Mathematics and Applications, Hebei Normal University, Shijiazhuang, 050024, People’s Republic of China
  • Email: yjzhu@mail.hebtu.edu.cn
  • Received by editor(s): April 4, 2012
  • Received by editor(s) in revised form: November 1, 2012
  • Published electronically: March 14, 2014
  • Additional Notes: The second author was supported by NSFC (No: 11371120), NSFC (No: 11071054), NCET (No: 11-0935), the Key Project of Chinese Ministry of Education (No: 211020), the Plan of Prominent Personnel Selection and Training for the Higher Education Disciplines in Hebei Province (BR2-219) and the SRF for ROCS, SEM
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 366 (2014), 3787-3804
  • MSC (2010): Primary 37D30; Secondary 37C20, 37B40
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06037-6
  • MathSciNet review: 3192618