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- W3104680055 abstract "Let $A$ be a finite alphabet and $f:~A^{ast }rightarrow A^{ast }$ be a morphism with an iterative fixed point $f^{{itomega}}({italpha})$ , where ${italpha}in A$ . Consider the subshift $({mathcal{X}},T)$ , where ${mathcal{X}}$ is the shift orbit closure of $f^{{itomega}}({italpha})$ and $T:~{mathcal{X}}rightarrow {mathcal{X}}$ is the shift map. Let $S$ be a finite alphabet that is in bijective correspondence via a mapping $c$ with the set of non-empty suffixes of the images $f(a)$ for $ain A$ . Let ${mathcal{S}}subset S^{mathbb{N}}$ be the set of infinite words $mathbf{s}=(s_{n})_{ngeq 0}$ such that ${itpi}(mathbf{s}):=c(s_{0})f(c(s_{1}))f^{2}(c(s_{2}))cdots in {mathcal{X}}$ . We show that if $f$ is primitive, $f^{{itomega}}({italpha})$ is aperiodic, and $f(A)$ is a suffix code, then there exists a mapping $H:~{mathcal{S}}rightarrow {mathcal{S}}$ such that $({mathcal{S}},H)$ is a topological dynamical system and ${itpi}:~({mathcal{S}},H)rightarrow ({mathcal{X}},T)$ is a conjugacy; we call $({mathcal{S}},H)$ the suffix conjugate of $({mathcal{X}},T)$ . In the special case where $f$ is the Fibonacci or Thue–Morse morphism, we show that the subshift $({mathcal{S}},T)$ is sofic, that is, the language of ${mathcal{S}}$ is regular." @default.
- W3104680055 created "2020-11-23" @default.
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- W3104680055 date "2014-06-04" @default.
- W3104680055 modified "2023-09-23" @default.
- W3104680055 title "Suffix conjugates for a class of morphic subshifts" @default.
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- W3104680055 doi "https://doi.org/10.1017/etds.2014.5" @default.
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