The topological Markov chain |
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Authors: | Zhou Zuoling |
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Affiliation: | (1) Zhongshan University, Zhongshan, China |
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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. This work is supported in part by the Foundation of Advanced Research Centre, Zhongshan University. |
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