The Hausdorff dimension of multiply Xiong chaotic sets

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.

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Published inErgodic theory and dynamical systems Vol. 40; no. 11; pp. 3056 - 3077
Main Authors LI, JIAN, LÜ, JIE, XIAO, YUANFEN
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.11.2020
Subjects
Original Article
multiply proximal cells
Gauss system
Hausdorff dimension
54H20
37B10
symbolic systems
37B99
multiply Xiong chaos
37B05
Online AccessGet full text
ISSN0143-3857
1469-4417
DOI10.1017/etds.2019.35

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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.
AbstractList 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.
Author LÜ, JIE
LI, JIAN
XIAO, YUANFEN
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  organization: 1Department of Mathematics, Shantou University, Shantou515063, Guangdong, China email lijian09@mail.ustc.edu.cn
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  givenname: JIE
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  surname: XIAO
  fullname: XIAO, YUANFEN
  email: xyuanfen@mail.ustc.edu.cn
  organization: 3Department of Mathematics, University of Science and Technology of China, Hefei 230026, Anhui, China email xyuanfen@mail.ustc.edu.cn
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Cites_doi 10.1016/j.jmaa.2014.04.026
10.1088/0951-7715/17/4/006
10.1007/s00220-010-1085-9
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10.1016/j.aim.2016.10.029
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10.1007/s00605-005-0356-6
10.1017/S0143385710000982
10.1088/0951-7715/16/4/313
10.1016/j.jde.2019.01.018
10.4064/cm110-2-3
10.3934/dcds.2004.10.827
10.1016/j.jnt.2016.10.019
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Issue 11
Keywords multiply proximal cells
Gauss system
Hausdorff dimension
54H20
37B10
symbolic systems
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multiply Xiong chaos
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