Digital expansions with negative real bases
Résumé
Similarly to Parry's characterization of $\beta$-expansions of real numbers in real bases $\beta > 1$, Ito and Sadahiro characterized digital expansions in negative bases, by the expansions of the endpoints of the fundamental interval. Parry also described the possible expansions of $1$ in base $\beta > 1$. In the same vein, we characterize the sequences that occur as $(-\beta)$-expansion of $\frac{-\beta}{\beta+1}$ for some $\beta > 1$. These sequences also describe the itineraries of $1$ by linear mod one transformations with negative slope.
Origine : Fichiers produits par l'(les) auteur(s)
Loading...