Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

Abstract : S-adic and substitutive systems have a rich theory in both the one-dimensional and multi-dimensional settings. With the hope of recovering these tools for group actions, in this talk, I will show how we can expand the notion of substitutions to countable groups. I will explore how different classes of groups admit different kinds of hierarchical decompositions that allow for the definition of S-adic and substitutive subshifts. I will then show how to recover classical results on minimality, zero entropy and unique ergodicity, provided the underlying group has good combinatorial properties. This is joint work with Christopher Cabezas and Pierre Guillon.