Measure transfer and S-adic developments for subshifts

Based on previous work of the authors, to any S-adic development of a subshift X a 'directive sequence' of commutative diagrams is associated, which consists at every level n >= 0 of the measure cone and the letter frequency cone of the level subshift X-n associated canonically to the given S-adic development. The issuing rich picture enables one to deduce results about X with unexpected directness. For instance, we exhibit a large class of minimal subshifts with entropy zero that all have infinitely many ergodic probability measures. As a side result, we also exhibit, for any integer d >= 2, an S-adic development of a minimal, aperiodic, uniquely ergodic subshift X, where all level alphabets A(n) have cardinality d, while none of the d - 2 bottom level morphisms is recognizable in its level subshift X-n subset of A(n)(Z).