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 give an $\mathcal{S}$-adic characterization of this family by means of two finite graphs. As an application, we are able to decide whether a shift space generated by a uniformly recurrent morphic word is (eventually) dendric.

翻译：树枝移位是通过其语言中单词扩展的组合限制来定义的。该族推广了著名的移位族，如Sturmian移位、Arnoux-Rauzy移位以及区间交换变换的编码。已知任何极小树枝移位均具有原始$\mathcal{S}$-adic表示，其中$\mathcal{S}$中的态射是由字母表生成的自由群上的正驯服自同构。本文通过两个有限图给出了该族的$\mathcal{S}$-adic特征刻画。作为应用，我们能够判定由一致递归形态词生成的移位空间是否为（最终）树枝的。