Topological Entropy of a Class of Subshifts of Finite Type
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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.
KeywordsSymbolic dynamical system subshift of finite type topological entropy transfer matrix Toeplitz matrix
MR(2010) Subject Classification54H20 37B10 37B40
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We thank the referees for their useful comments.
- Zhou, Z. L., Yin, J. D., Xu, S. Y.: Topological Dynamical Systems–From Topology to Ergodic Theory, the Modern Mathematical Basis Books (Chinese Edition), Science Press, Beijing, 2011Google Scholar