Ito-Sadahiro numbers vs. Parry numbers

Abstract

We consider positional numeration system with negative base, as introduced by Ito and Sadahiro. In particular, we focus on algebraic properties of negative bases $-\beta$ for which the corresponding dynamical system is sofic, which happens, according to Ito and Sadahiro, if and only if the $(-\beta )$-expansion of $-\frac{\beta }{\beta +1}$ is eventually periodic. We call such numbers $\beta$ Ito-Sadahiro numbers and we compare their properties with Parry numbers, occurring in the same context for Rényi positive base numeration system.

10 pages