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Acta Mathematica Sinica, English Series

, Volume 34, Issue 12, pp 1765–1777 | Cite as

Topological Entropy of a Class of Subshifts of Finite Type

  • Jin Zhong Xu
  • Lan Yu Wang
Article
  • 54 Downloads

Abstract

In this paper, we construct a special class of subshifts of finite type. By studying the spectral radius of the transfer matrix associated with the subshift of finite type, we obtain an estimation of its topological entropy. Interestingly, we find that the topological entropy of this class of subshifts of finite type converges monotonically to log(n + 1) (a constant only depends on the structure of the transfer matrices) as the increasing of the order of the transfer matrices.

Keywords

Symbolic dynamical system subshift of finite type topological entropy transfer matrix Toeplitz matrix 

MR(2010) Subject Classification

54H20 37B10 37B40 

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Notes

Acknowledgements

We thank the referees for their useful comments.

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Key Laboratory of Space Utilization, Technology and Engineering Center for Space UtilizationChinese Academy of SciencesBeijingP. R. China
  2. 2.University of Chinese Academy of SciencesBeijingP. R. China
  3. 3.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingP. R. China

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