Tower power for S-adics

We explain and restate the results from our recent paper [ 2 ] 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...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2021-04, Vol.297 (3-4), p.1853-1875
Main Authors: Bédaride, Nicolas, Hilion, Arnaud, Lustig, Martin
Format: Article
Language:English
Subjects:
Combinatorics
Computer Science
Discrete Mathematics
Dynamical Systems
Mathematics
Mathematics and Statistics
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Summary:We explain and restate the results from our recent paper [ 2 ] 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 ∈ A ∗ and any invariant measure μ on the subshift X σ defined by any everywhere growing but not necessarily primitive or irreducible substitution σ : A ∗ → A ∗ . Several examples are considered in detail, and model computations are presented.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-020-02582-w