The \(S\)-adic Pisot conjecture on two letters (Q281757)

The Pisot conjecture relates the property of pure discrete spectrum for substitution dynamical systems to arithmetic properties of its expansion factor. Here an extension of the Pisot conjecture on two symbols is shown in the symbolic \(S\)-adic framework, roughly speaking for infinite words obtained obtained by iterating different substitutions in a prescribed order. In this setting there is no natural canonical stable space, and the arguments in the proofs involve combinatorial properties of the resulting sequences and properties of associated Rauzy fractals.