Intermediate $\beta$-shifts of finite type
| Autor: | Tony Samuel, Bing Li, Tuomas Sahlsten |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Physics
Mathematics - Number Theory Applied Mathematics 010102 general mathematics Primary: 37B10 58F17 Secondary: 11A67 11R06 02 engineering and technology Type (model theory) Subshift of finite type 01 natural sciences Combinatorics 0202 electrical engineering electronic engineering information engineering Discrete Mathematics and Combinatorics 020201 artificial intelligence & image processing Beta (velocity) Mathematics - Dynamical Systems 0101 mathematics Analysis |
| Zdroj: | Li, B, Sahlsten, T & Samuel, T 2016, ' Intermediate beta-shifts of finite type ', Discrete and Continuous Dynamical Systems, vol. 36, no. 1, pp. 323-344 . https://doi.org/10.3934/dcds.2016.36.323 |
| ISSN: | 1078-0947 |
| DOI: | 10.3934/dcds.2016.36.323 |
| Popis: | An aim of this article is to highlight dynamical differences between the greedy, and hence the lazy, $\beta$-shift (transformation) and an intermediate $\beta$-shift (transformation), for a fixed $\beta \in (1, 2)$. Specifically, a classification in terms of the kneading invariants of the linear maps $T_{\beta,\alpha} \colon x \mapsto \beta x + \alpha \bmod 1$ for which the corresponding intermediate $\beta$-shift is of finite type is given. This characterisation is then employed to construct a class of pairs $(\beta,\alpha)$ such that the intermediate $\beta$-shift associated with $T_{\beta, \alpha}$ is a subshift of finite type. It is also proved that these maps $T_{\beta,\alpha}$ are not transitive. This is in contrast to the situation for the corresponding greedy and lazy $\beta$-shifts and $\beta$-transformations, for which both of the two properties do not hold. Comment: v3: 19 pages, 6 figures, fixed typos and minor errors, to appear in Discrete Contin. Dyn. Syst. A |
| Databáze: | OpenAIRE |
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