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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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Partial hyperbolicity and specification
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by Naoya Sumi, Paulo Varandas and Kenichiro Yamamoto PDF
Proc. Amer. Math. Soc. 144 (2016), 1161-1170 Request permission

Abstract:

We study the specification property for partially hyperbolic dynamical systems. In particular, we show that if a partially hyperbolic diffeomorphism has two saddles with different indices, and the stable manifold of one of these saddles coincides with the strongly stable leaf, then it does not satisfy the specification property.
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Additional Information
  • Naoya Sumi
  • Affiliation: Department of Mathematics, Faculty of Science, Kumamoto University, 2-39-1 Kurokami, Kumamoto-shi, Kumamoto, 860-8555, Japan
  • MR Author ID: 610209
  • Email: sumi@sci.kumamoto-u.ac.jp
  • Paulo Varandas
  • Affiliation: Departamento de Mathemática, Universidade Federal da Bahia, Ademar de barros S/N, 20170-110 Sulvador, Brazil
  • MR Author ID: 857790
  • Email: paulo.varandas@ufba.br
  • Kenichiro Yamamoto
  • Affiliation: Department of General Education, Nagaoka University of Technology, Niigata 940-2188, Japan
  • MR Author ID: 878580
  • Email: k_yamamoto@vos.nagaokaut.ac.jp
  • Received by editor(s): October 13, 2014
  • Received by editor(s) in revised form: February 26, 2015
  • Published electronically: August 20, 2015
  • Communicated by: Yingfei Yi
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 1161-1170
  • MSC (2010): Primary 37D25, 37D30
  • DOI: https://doi.org/10.1090/proc/12830
  • MathSciNet review: 3447669