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Periodic points for amenable group actions on uniquely arcwise connected continua

Part of: Special properties Topological dynamics

Published online by Cambridge University Press:  30 September 2020

ENHUI SHI  and
XIANGDONG YE
ENHUI SHI
Affiliation:
School of Mathematical Sciences, Soochow University, Suzhou 215006, P. R. China (e-mail: ehshi@suda.edu.cn)
XIANGDONG YE
Affiliation:
Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences and Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China (e-mail: yexd@ustc.edu.cn)
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Abstract

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We show that any action of a countable amenable group on a uniquely arcwise connected continuum has a periodic point of order $\leq 2$.

Keywords

amenable groupperiodic pointdendritecontinuum

MSC classification

Primary: 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)
Secondary: 54F50: Spaces of dimension $leq 1$; curves, dendrites

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 9 , September 2021 , pp. 2833 - 2844
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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