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The topological Markov chain

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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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References

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Authors and Affiliations

  1. Zhongshan University, Zhongshan, China

    Zhou Zuoling

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  1. Zhou Zuoling
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Additional information

This work is supported in part by the Foundation of Advanced Research Centre, Zhongshan University.

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Zuoling, Z. The topological Markov chain. Acta Mathematica Sinica 4, 330–337 (1988). https://doi.org/10.1007/BF02560636

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  • DOI: https://doi.org/10.1007/BF02560636

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