Complete Characterization of Substitution Invariant Sturmian Sequences

We provide a complete characterization of substitution invariant inhomogeneous bidirectional pointed Sturmian sequences. The result is analogous to that obtained by Berth´e et al. [5] and Yasutomi [21] for one-directional Sturmian words. The proof is constructive, based on the geometric representation of Sturmian words by a cut-and-project scheme