%0 Journal Article %A Zhou Zuoling %T The Topological Markov Chain* %D 1988 %R 10.1007/BF02560636 %J Acta Mathematica Sinica %P 330-337 %V 4 %N 4 %X 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. %U https://actamath.cjoe.ac.cn/Jwk_sxxb_en/EN/10.1007/BF02560636