adic characterization of minimal ternary dendric shifts

Abstract Dendric shifts are defined by combinatorial restrictions of the extensions of the words in their languages. This family generalizes well-known families of shifts such as Sturmian shifts, Arnoux–Rauzy shifts and codings of interval exchange transformations. It is known that any minimal dendr...

Full description

Saved in:
Bibliographic Details
Published inErgodic theory and dynamical systems Vol. 42; no. 11; pp. 3393 - 3432
Main Authors GHEERAERT, FRANCE, LEJEUNE, MARIE, LEROY, JULIEN
Format Journal Article
LanguageEnglish
Published 01.11.2022
Online AccessGet full text

Cover

More Information
Summary:Abstract Dendric shifts are defined by combinatorial restrictions of the extensions of the words in their languages. This family generalizes well-known families of shifts such as Sturmian shifts, Arnoux–Rauzy shifts and codings of interval exchange transformations. It is known that any minimal dendric shift has a primitive $\mathcal {S}$ -adic representation where the morphisms in $\mathcal {S}$ are positive tame automorphisms of the free group generated by the alphabet. In this paper, we investigate those $\mathcal {S}$ -adic representations, heading towards an $\mathcal {S}$ -adic characterization of this family. We obtain such a characterization in the ternary case, involving a directed graph with two vertices.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2021.84