The Topological Markov Chain<sup>*</sup>
Acta Mathematica Sinica, English Series
HOME| ABOUT JOURNAL | EDITORIAL BOARD | FOR AUTHORS| SUBSCRIPTIONS| ADVERTISEMENT| CONTACT US
 
Acta Mathematica Sinica,
Chinese Series
 
   
   
Adv Search »  
Acta Mathematica Sinica, English Series  1988, Vol. 4 Issue (4): 330-337    DOI: 10.1007/BF02560636
articles Current Issue | Next Issue | Archive | Adv Search  |   
The Topological Markov Chain*
Zhou Zuoling
Zhongshan University
 Download: PDF (2679 KB)   HTML (0 KB)   Export: BibTeX | EndNote (RIS)      Supporting Info
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.

Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Zhou Zuoling
Key words:   
Received: 1986-11-10;
Fund: *This work is supported in part by the Foundation of Advanced Research Centre,Zhongshan University.
Cite this article:   
Zhou Zuoling. The Topological Markov Chain*[J]. Acta Mathematica Sinica, English Series, 1988, 4(4): 330-337.
URL:  
http://www.actamath.com/Jwk_sxxb_en//EN/10.1007/BF02560636      or     http://www.actamath.com/Jwk_sxxb_en//EN/Y1988/V4/I4/330
 
[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.
No Similar of article
  Copyright 2012 © Editorial Office of Acta Mathematica Sinica
京ICP备05002806号-7