Tower power for $S$-adics
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866910627634610176 |
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| author | Bédaride, Nicolas Hilion, Arnaud Lustig, Martin |
| author_facet | Bédaride, Nicolas Hilion, Arnaud Lustig, Martin |
| contents | We explain and restate the results from our recent paper arXiv:1503.08000.v3 in standard language for substitutions and $S$-adic systems in symbolic dynamics. We then produce as rather direct application an $S$-adic system (with finite set of substitutions $S$ on $d$ letters) that is minimal and has $d$ distinct ergodic probability measures.
As second application we exhibit a formula that allows an efficient practical computation of the cylinder measure $μ([w])$, for any word $w \in \cal A^*$ and any invariant measure $μ$ on the subshift $X_σ$ defined by any everywhere growing but not necessarily primitive or irreducible substitution $σ: \cal A^* \to \cal A^*$. Several examples are considered in detail, and model computations are presented. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1902_04904 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Tower power for $S$-adics Bédaride, Nicolas Hilion, Arnaud Lustig, Martin Dynamical Systems 37B10, 37A25, 37E25 We explain and restate the results from our recent paper arXiv:1503.08000.v3 in standard language for substitutions and $S$-adic systems in symbolic dynamics. We then produce as rather direct application an $S$-adic system (with finite set of substitutions $S$ on $d$ letters) that is minimal and has $d$ distinct ergodic probability measures. As second application we exhibit a formula that allows an efficient practical computation of the cylinder measure $μ([w])$, for any word $w \in \cal A^*$ and any invariant measure $μ$ on the subshift $X_σ$ defined by any everywhere growing but not necessarily primitive or irreducible substitution $σ: \cal A^* \to \cal A^*$. Several examples are considered in detail, and model computations are presented. |
| title | Tower power for $S$-adics |
| topic | Dynamical Systems 37B10, 37A25, 37E25 |
| url | https://arxiv.org/abs/1902.04904 |