On the topological entropy of the subshifts of finite type on free semigroups

Date(s) : 06/02/2018
11 h 00 min - 12 h 00 min

In this talk, we provide an effective method to compute the topological entropies of G-subshifts of finite type (G-SFTs) with G = Fd or Sd, i.e., the free group and semigroup with d generators. We set up the topological entropy theory by analyzing the corresponding systems of nonlinear recursive equations (SNREs). Four types of SNREs of S2-SFTs, namely the types E, D, C and O, are introduced and we could compute their topological entropies explicitly. This enables us to give the complete characterization of S2-SFTs on two symbols. That is, the set of topological entropies of S2-SFTs on two symbols is equal to the union of E, D, U and O. We note that there is an example in type O of S2-SFT on two symbols such that the topological entropy is not well-defined. This gives an affirmative answer to the problem raised by Petersen-Salama in 2017. The methods developed in Sd-SFTs will also be applied to the study the topological entropy theory of Fd-SFTs. Finally, the topological entropy formulas of Sd-, Fd-golden mean shifts and k-colored chessboards are also presented herein.



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