Dynamics and entropy of $\mathcal{S}$-graph shifts
| Autor: | Dillon, Travis |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | $S$-gap shifts are a well-studied class of shift spaces, which has led to several proposed generalizations. This paper introduces a new class of shift spaces called $\mathcal{S}$-graph shifts whose essential structure is encoded in a novel way, as a finite directed graph with a set of natural numbers assigned to each vertex. $\mathcal{S}$-graph shifts contain $S$-gap shifts and their generalizations, as well as all vertex shifts and SFTs, as special cases, thereby providing a method to study these shift spaces in a uniform way. The main result in this paper is a formula for the entropy of any $\mathcal{S}$-graph shift, which, by specialization, resolves a problem proposed by Matson and Sattler. A second result establishes an explicit formula for the zeta functions of $\mathcal{S}$-graph shifts. Additionally, we show that every entropy value is obtained by uncountably many $\mathcal{S}$-graph shifts. Comment: 26 pages. Added sections zeta function and intrinsic ergodicity; removed the section on generalization of $\mathcal{S}$-graph shifts; moved several proofs to an appendix |
| Databáze: | arXiv |
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