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Relative bifurcation sets and the local dimension of univoque bases
Published online by Cambridge University Press: 26 May 2020
Abstract
Fix an alphabet $A=\{0,1,\ldots ,M\}$ with $M\in \mathbb{N}$. The univoque set $\mathscr{U}$ of bases $q\in (1,M+1)$ in which the number $1$ has a unique expansion over the alphabet $A$ has been well studied. It has Lebesgue measure zero but Hausdorff dimension one. This paper describes how the points in the set $\mathscr{U}$ are distributed over the interval $(1,M+1)$ by determining the limit
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