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

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Showing 2023Show all

2 papers · 1 filter

math.PR2023

Random subsets of Cantor sets generated by trees of coin flips

Pieter Allaart, Taylor Jones

We introduce a natural way to construct a random subset of a homogeneous Cantor set $C$ in $[0, 1]$ via random labelings of an infinite $M$ -ary tree, where $M \geq 2$ . The Cantor set…

math.DS2023

Entropy plateaus, transitivity and bifurcation sets for the $β$ -transformation with a hole at $0$

Pieter Allaart, Derong Kong

Given $β > 1$ , 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 all $x…

Random subsets of Cantor sets generated by trees of coin flips

Entropy plateaus, transitivity and bifurcation sets for the β-transformation with a hole at 0

Entropy plateaus, transitivity and bifurcation sets for the $β$ -transformation with a hole at $0$