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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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Some properties of coupled-expanding maps in compact sets
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by Xu Zhang, Yuming Shi and Guanrong Chen PDF
Proc. Amer. Math. Soc. 141 (2013), 585-595 Request permission

Abstract:

In this paper, some properties of a strictly $A$-coupled-expanding map in compact subsets of a metric space are studied, where $A$ is a transition matrix. It is shown that this map has a compact invariant set on which it is topologically semi-conjugate to the subshift for $A$. If the subshift for $A$ has positive topological entropy, then the map is chaotic in the sense of Li-Yorke. Moreover, in the one-dimensional case, the map is at most two-to-one conjugate to the subshift for $A$ and chaotic in the sense of Devaney.
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Additional Information
  • Xu Zhang
  • Affiliation: Department of Mathematics, Shandong University, Jinan, Shandong 250100, People’s Republic of China
  • Email: xuzhang08@gmail.com
  • Yuming Shi
  • Affiliation: Department of Mathematics, Shandong University, Jinan, Shandong 250100, People’s Republic of China
  • Email: ymshi@sdu.edu.cn
  • Guanrong Chen
  • Affiliation: Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, People’s Republic of China
  • Email: eegchen@cityu.edu.hk
  • Received by editor(s): November 8, 2010
  • Received by editor(s) in revised form: July 2, 2011
  • Published electronically: June 19, 2012
  • Additional Notes: This research was partially supported by the RFDP of Higher Education of China (Grant 2010013 1110024) and the NNSF of China (Grant 11071143), the Hong Kong Research Council under Grant CityU 117/10E, and the Graduate Innovation Fund of Shandong University (Grant 11140070613137).
  • Communicated by: Yingfei Yi
  • © Copyright 2012 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 585-595
  • MSC (2010): Primary 37D45; Secondary 37B10
  • DOI: https://doi.org/10.1090/S0002-9939-2012-11339-5
  • MathSciNet review: 2996963