题目：On the topological entropy of the subshifts of finite type on free semigroups
摘要：In this talk, we provide an effective method to compute the topological entropies of G-subshifts of finite type (G-SFTs) with G = F_d or S_d, i.e., the free and free semigroups 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 S_2-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 S_2-SFTs on two symbols. That is, the set of topological entropies of S_2-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 S_2-SFT on two symbols such that the topological entropy is not well-defined. The methods developed in S_d-SFTs will also be applied to the study the topological entropy theory of F_d-SFTs. Finally, the topological entropy formulas of S_d-, F_d-golden mean shifts and k-colored chessboards are also presented herein.
时 间: 2018年1月22号下午15:00-17:00
地 点: 蒙民伟楼1105