2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68315Consider the minimal $β$-shift containing the shift space generated by given Sturmian word. In this paper we characterize such $β$ and investigate its combinatorial, dynamical and topological properties and prove that such $β$ are transcendental numbers.21 pages, LatexCombinatoricsDynamical SystemsNumber Theory68R15; 11J91; 37B10text