Measure transfer and $S$-adic developments for subshifts
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910819217833984 |
|---|---|
| author | Bédaride, Nicolas Hilion, Arnaud Lustig, Martin |
| author_facet | Bédaride, Nicolas Hilion, Arnaud Lustig, Martin |
| contents | 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 $X_n \subset {\cal A}_n^\mathbb Z$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_11235 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Measure transfer and $S$-adic developments for subshifts Bédaride, Nicolas Hilion, Arnaud Lustig, Martin Dynamical Systems 37B10 (Primary) 37A25, 37E25 (Secondary) 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 $X_n \subset {\cal A}_n^\mathbb Z$. |
| title | Measure transfer and $S$-adic developments for subshifts |
| topic | Dynamical Systems 37B10 (Primary) 37A25, 37E25 (Secondary) |
| url | https://arxiv.org/abs/2211.11235 |