Topology of univoque sets in real base expansions

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Topology of univoque sets in real base expansions
Martedì 17 maggio 2022 alle ore 14:30, presso il Dipartimento di Matematica e Fisica (Aula 311), si terrà il seminario del prof. Vilmos Komornik (Université de Strasbourg) dal titolo "Topology of univoque sets in real base expansions".

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We report on a recent joint paper with Martijn de Vries and Paola Loreti. Given a positive integer M and a real number 1 < q ≤ M+1, an expansion of a real number x ∈ [0,M/(q-1)] over the alphabet A = {0,1,...,M} is a sequence (c_i) ∈ A^N such that x = Σ_{k=1}^∞ c_i q^{-i}. Generalizing many earlier results, we investigate the topological properties of the set Uq consisting of numbers x having a unique expansion of this form, and the combinatorial properties of the set U'q consisting of their corresponding expansions.

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