P. Allaart

activity

20062023

most citedOn the continuity of the Hausdorff dimension of the univoque set

17 citations · 59 across the 22 of their papers we have counts for

collaborators

Showing 2020Show all

2 papers · 1 filter

math.DS2020

Density spectrum of Cantor measure

Pieter Allaart, Derong Kong

Given $ρ \in (0, 1/3]$ , let $μ$ be the Cantor measure satisfying $μ = \frac{1}{2} μ f_{0}^{- 1} + \frac{1}{2} μ f_{1}^{- 1}$ , where $f_{i} (x) = ρ x + i (1 - ρ)$ for $i = 0, 1$ . The support of $μ$ is a Cantor…

math.NT2020★ 1 cited

On the smallest base in which a number has a unique expansion

Pieter Allaart, Derong Kong

Given a real number $x > 0$ , we determine $q_{s} (x) := in f U (x)$ , where $U (x)$ is the set of all bases $q \in (1, 2]$ for which $x$ has a unique expansion of $0$ 's and $…