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- W1967637841 abstract "Let $S={s_iinmathbb Ncup{0}:0leq s_i<s_{i+1}}$ and let $d_{0}=s_{0}$ and $Delta(S)={d_{n}}_{n}$ where $d_{n}=s_{n}-s_{n-1}$. In this note, we show that an $S$-gap shift is subshift of finite type (SFT) if and only if $S$ is finite or cofinite, is almost-finite-type (AFT) if and only if $Delta(S)$ is eventually constant and is sofic if and only if $Delta(S)$ is eventually periodic. We also show that there is a one-to-one correspondence between the set of all $S$-gap shifts and ${r in mathbb R: r geq 0}backslash {frac{1}{n}: n in {mathbb N}}$ up to conjugacy. This enables us to induce a topology and measure structure on the set of all $S$-gaps. By using this, we give the frequency of certain $S$-gap shifts with respect to their dynamical properties." @default.
- W1967637841 created "2016-06-24" @default.
- W1967637841 creator A5072583380 @default.
- W1967637841 creator A5076417802 @default.
- W1967637841 date "2011-08-16" @default.
- W1967637841 modified "2023-10-14" @default.
- W1967637841 title "Dynamics and Topology of S-gap Shifts" @default.
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- W1967637841 doi "https://doi.org/10.48550/arxiv.1108.3242" @default.
- W1967637841 hasPublicationYear "2011" @default.
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