Digital expansions with negative real bases
Abstract
Similarly to Parry's characterization of β-expansions of real numbers in real bases β > 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 β > 1. In the same vein, we characterize the sequences that occur as (-β)-expansion of -ββ+1 for some β > 1. These sequences also describe the itineraries of 1 by linear mod one transformations with negative slope.
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