STURMIAN WORDS AND β-SHIFTS: DYNAMICS AND

Abstract. For a given Sturmian word s, we consider the minimal β-shift containing the shift space generated by s. In this note we characterize such β, and investigate its dynamical, topological and number theoretical properties. 1. Introduction. Sturmian words are infinite words over binary alphabet A whose factors of length n are exactly n + 1. It is known that Sturmian words are aperiodic infinite words with minimal complexity [8]. These critical words admit some equivalent definitions in different manners. They can be coded from the irrational billiards on a uni