P. Allaart

activity

20242026

collaborators

3 papers

math.DS2026

Critical values for the $I^^{2}$ -transformation with a hole at $0$

Pieter Allaart, Derong Kong

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

math.DS2025

Entropy plateaus, transitivity and bifurcation sets for the $I^^{2}$ -transformation with a hole at $0$

Pieter Allaart, Derong Kong

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

math.PR2024

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…

Critical values for the I^2-transformation with a hole at 0

Entropy plateaus, transitivity and bifurcation sets for the I^2-transformation with a hole at 0

Random subsets of Cantor sets generated by trees of coin flips

Critical values for the $I^^{2}$ -transformation with a hole at $0$

Entropy plateaus, transitivity and bifurcation sets for the $I^^{2}$ -transformation with a hole at $0$