S-adic characterization of dendric languages: ternary case

Uniformly recurrent dendric languages generalize Arnoux-Rauzy languages and interval exchanges and are defined via the left-, right- and biextensions of their words. In a series of articles, Berthé et al. introduced them and, among other results, proved that this family is stable under derivation, which leads to the existence of particular S-adic representations. In this talk, we see how we can use the properties of these representations to obtain an S-adic characterization of uniformly recurrent dendric languages. We give some general results then focus on the case of a ternary alphabet to obtain a simpler characterization. This is a joint work with Marie Lejeune and Julien Leroy.