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The Hausdorff dimension of multiply Xiong chaotic sets

Part of: Connections with other structures, applications Topological dynamics

Published online by Cambridge University Press:  06 June 2019

JIAN LI Open the ORCID record for JIAN LI [Opens in a new window] ,
JIE LÜ  and
YUANFEN XIAO Open the ORCID record for YUANFEN XIAO [Opens in a new window]
JIAN LI
Affiliation:
Department of Mathematics, Shantou University, Shantou515063, Guangdong, China email lijian09@mail.ustc.edu.cn
JIE LÜ
Affiliation:
School of Mathematics, South China Normal University, Guangzhou510631, China email ljie@scnu.edu.cn
YUANFEN XIAO
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei 230026, Anhui, China email xyuanfen@mail.ustc.edu.cn
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Abstract

We construct a multiply Xiong chaotic set with full Hausdorff dimension everywhere that is contained in some multiply proximal cell for the full shift over finite symbols and the Gauss system, respectively.

Keywords

multiply Xiong chaosmultiply proximal cellssymbolic systemsGauss systemHausdorff dimension

MSC classification

Primary: 54H20: Topological dynamics 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.) 37B10: Symbolic dynamics
Secondary: 37B99: None of the above, but in this section
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 11 , November 2020 , pp. 3056 - 3077
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Copyright
© Cambridge University Press, 2019

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