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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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Monotone maps of $G$-like continua with positive topological entropy yield indecomposability
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by Hisao Kato PDF
Proc. Amer. Math. Soc. 147 (2019), 4363-4370 Request permission

Abstract:

In the previous paper Adv. Math. 304 (2017), pp. 793–808, we proved that if for any graph $G$, a homeomorphism on a $G$-like continuum $X$ has positive topological entropy, then the continuum $X$ contains an indecomposable subcontinuum. Also, if for a tree $G$, a monotone map on a $G$-like continuum $X$ has positive topological entropy, then the continuum $X$ contains an indecomposable subcontinuum. In this note, we extend these results. In fact, we prove that if for any graph $G$, a monotone map on a $G$-like continuum $X$ has positive topological entropy, then the continuum $X$ contains an indecomposable subcontinuum. Also we study topological entropy of monotone maps on Suslinean continua.
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Additional Information
  • Hisao Kato
  • Affiliation: Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571 Japan
  • MR Author ID: 200384
  • Email: hkato@math.tsukuba.ac.jp
  • Received by editor(s): September 21, 2016
  • Received by editor(s) in revised form: January 14, 2019
  • Published electronically: April 18, 2019
  • Communicated by: Nimish Shah
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4363-4370
  • MSC (2010): Primary 37B45, 37B40; Secondary 54H20, 54F15
  • DOI: https://doi.org/10.1090/proc/14602
  • MathSciNet review: 4002548