The Topological Markov Chain<sup>*</sup>
Acta Mathematica Sinica, English Series
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Acta Mathematica Sinica, English Series  1988, Vol. 4 Issue (4): 330-337    DOI: 10.1007/BF02560636
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The Topological Markov Chain*
Zhou Zuoling
Zhongshan University
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Abstract The topological Markov chain or the subshift of finite type is a restriction of the shift on an invariant subset determined by a 0,1-matrix,which has some important applications in the theory of dynamical systems.

In this paper,the topological Markov chain has been discussed.First,we introduce a structure of the directed gragh on a 0,1-matrix,and then by using it as a tool,we give some equivalent conditions with respect to the relationship among topological entropy,chaos,the nonwandering set,the set of periodic points and the 0,1-matrix involved.

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Received: 1986-11-10;
Fund: *This work is supported in part by the Foundation of Advanced Research Centre,Zhongshan University.
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Zhou Zuoling. The Topological Markov Chain*[J]. Acta Mathematica Sinica, English Series, 1988, 4(4): 330-337.
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[1] Li,T.Y.and Yorke,J.A.,Period three implies chaos,Amer.Math.Monthly,82(1975),985-992.
[2] Zhou Zuoling,A note on the Li-Yorke's theorem,Kexue Tongbao (English ed.),31(1986),10:649-651.
[3] -,Chaos and totally chaos,Kexue Tongbao,(Chinese ed.),32(1987),4:248-250.
[4] -,Chaotic behavior of the one sided shift,Acta Mathematica Sinica (Chinese ed.),30(1987),2:284-288.
[5] Walters,P.,An Introduction to Ergodic Theory,p.178,Springer-Verlag,New-York Heidelberg Berlin,1982.
[6] Bowen,R.,Topological entropy and axim A,Global Analysis,Vol.14,p.37.
[7] Zhou Zuoling,Chaotic behavior of the two sided shift,ChineseAnnals of Mathematics (Series A),8A(6)(1987),677-681.
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