Univoque bases of real numbers: local dimension, Devil's staircase and isolated points

Abstract: Given a positive integer $M$ and a real number $x$, let $U(x)$ be the set of all bases $q \in (1,M+1]$ such that $x$ has a unique $q$-expansion with respect to the alphabet $\{0,1,\dots,M\}$. We will investigate the local dimension of $U(x)$ and prove a 'variation principle' for unique non-integer base expansions. We will also determine the critical values and the topological structure of $U(x)$.

dynamical systemsnumber theory

Audience: researchers in the topic

One World Numeration seminar

Series comments: Description: Online seminar on numeration systems and related topics

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