Journal of Guangxi Normal University(Natural Science Edition) ›› 2013, Vol. 31 ›› Issue (4): 66-70.

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Distributional Chaotic Property of the Factor System of Symbolic Dynamical System

KANG Yun-lian, LIU Long-sheng, ZHAO Jun-ling   

  1. College of Mathematical Science,Guangxi Normal University,Guilin Guangxi 541004,China
  • Received:2013-08-05 Online:2013-12-20 Published:2018-11-26

Abstract: Let (Σ,σ) be a dynamical system which has two symbols,and (X,f) be a compact system.If there exists a continuous map h of Σ→X,such that h σ=f h,then (X,f) is the factor system of (Σ,σ).It is proved that if the factor system of (Σ,σ) is uncountable set,then it is distributionally chaotic.

Key words: symbolic dynamical system, factor system, distributional chaos

CLC Number: 

  • O19
[1] LI Tien-yien,YORKE J A.Period three implies chaos[J].Amer Math Monthly,1975,82(10):985-992.
[2] SCHWEIZER B,SMITAL J.Measure of chaos and a spectral decomposition of dynamical systems on the interval[J].Trans Amer Math Soc,1994,344(2):737-754.
[3] OPROCHA P.Relations between distributional and Devaney chaos[J].Chaos,2006,16(3):033112.
[4] LIAO Gong-fu,CHU Zhen-yan,FAN Qin-jie.Relations between mixing and distributional chaos[J].Chaos,Solitions and Fractals,2009,41(4):1994-2000.
[5] LI Shi-hai.ω-Chaos and topological entropy[J].Trans Amer Math Soc,1993,339(1):243-249.
[6] GENG Xiang-yi.Chaos for the factors of one-sides shift[J].Songliao Journal:Natural Science Edition,1999(1):18-19.
[7] 廖公夫,汪威,范钦杰.一类非本原代换与混沌[J].数学年刊,2009,30A(2):183-188.
[8] 周作领.符号动力系统[M].上海:上海科技教育出版社,1997:18-20.
[9] 范钦杰,王辉.强非游荡集与分布混沌(Ⅱ)[J].吉林大学学报:理学版,2012,50(2):278-280.
[10] 廖公夫,王立冬.几乎周期性与SS混沌集[J].数学年刊,2001,23A(6):685-692.
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[2] DENG Jin-hong, ZHAO Jun-ling. SS Chaotic Set in Set of Non-recurrent Points [J]. Journal of Guangxi Normal University(Natural Science Edition), 2011, 29(2): 40-44.
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