Measure transfer and $S$-adic developments for subshifts - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Measure transfer and $S$-adic developments for subshifts

Résumé

Based on previous work of the authors, to any $S$-adic development of a subshift $X$ a "directive sequence" of commutative diagrams is associated, which consists at every level $n \geq 0$ of the measure cone and the letter frequency cone of the level subshift $X_n$ associated canonically to the given $S$-adic development. The issuing rich picture enables one to deduce results about $X$ with unexpected directness. For instance, we exhibit a large class of minimal subshifts with entropy zero that all have infinitely many ergodic probability measures. As a side result we also exhibit, for any integer $d \geq 2$, an $S$-adic development of a minimal, aperiodic, uniquely ergodic subshift $X$, where all level alphabets ${\cal A}_n$ have cardinality $d\,$, while none of the $d-2$ bottom level morphisms is recognizable in its level subshift $X_n \subset {\cal A}_n^\mathbb Z$.

Dates et versions

hal-04053095 , version 1 (31-03-2023)

Identifiants

Citer

Nicolas Bédaride, Arnaud Hilion, Martin Lustig. Measure transfer and $S$-adic developments for subshifts. 2023. ⟨hal-04053095⟩
15 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More