Topology of univoque sets in real base expansions

Abstract: We report on a recent joint paper with Martijn de Vries and Paola Loreti. Given a positive integer $M$ and a real number $1 < q\le M+1$, an expansion of a real number $x \in \left[0,M/(q-1)\right]$ over the alphabet $A=\{0,1,\ldots,M\}$ is a sequence $(c_i) \in A^{\mathbb{N}}$ such that $x=\sum_{i=1}^{\infty}c_iq^{-i}$. Generalizing many earlier results, we investigate the topological properties of the set $U_q$ 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.

dynamical systemsnumber theory

Audience: researchers in the topic

( paper | slides )

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