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 2021Show all

2 papers · 1 filter

math.DS2021

Critical values for the $β$ -transformation with a hole at $0$

Pieter Allaart, Derong Kong

Given $β \in (1, 2]$ , let $T_{β}$ be the $β$ -transformation on the unit circle $[0, 1)$ such that $T_{β} (x) = β x (mod 1)$ . For each $t \in [0, 1)$ let $K_{β} (t)$ be the survivor set consisting of…

math.NT2021

On the existence of numbers with matching continued fraction and decimal expansions

Pieter Allaart, Stephen Jackson, Taylor Jones +1

A Trott number is a number $x \in (0, 1)$ whose continued fraction expansion is equal to its base $b$ expansion for a given base $b$ , in the following sense: If $x = [0; a_{1}, a_{2}, \dots]$ ,…

Critical values for the β-transformation with a hole at 0

On the existence of numbers with matching continued fraction and decimal expansions

Critical values for the $β$ -transformation with a hole at $0$