Abstract
Abstract This paper investigates representations of real numbers with an arbitrary negative base –β < –1, which we call the (–β)-expansions. They arise from the orbits of the (–β)-transformation which is a natural modification of the β-transformation. We show some fundamental properties of (–β)-expansions, each of which corresponds to a well-known fact of ordinary β-expansions. In particular, we characterize the admissible sequences of (–β)-expansions, give a necessary and sufficient condition for the (–β)-shift to be sofic, and explicitly determine the invariant measure of the (–β)-transformations.
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