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Universal Expansions in Negative and Complex Bases

Abstract Expansions in noninteger positive bases have been intensively investigated since the pioneering works of Rényi (Acta Math. Hungar. 8: 477–493, 1957) and Parry (Acta Math. Hungar. 11: 401–416, 1960). The discovery of surprising unique expansions in certain noninteger bases by Erdős, Horváth and Joó (Acta Math. Hungar. 58: 333–342, 1991) was followed by many studies aiming to clarify the topological and combinatorial nature of the sets of these bases. In the present work we extend some of these studies to more general, negative or complex bases.