Tower power for $S$-adics

Abstract

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 $\mu ([w])$, for any word $w\in {\mathcal{A}}^{\ast }$ and any invariant measure $\mu$ on the subshift $X_{\sigma }$ defined by any everywhere growing but not necessarily primitive or irreducible substitution $\sigma :{\mathcal{A}}^{\ast }\to {\mathcal{A}}^{\ast }$. Several examples are considered in detail, and model computations are presented.

20 pages. See also arXiv:1503.08000.v3

Cited by in corpus (2)

• Invariant measures on finite rank subshifts
• The measure transfer for subshifts induced by a morphism of free monoids