Pieter Allaart

collaborators

3 papers

math.DS2025

Equality of Hölder exponents for distribution functions of Gibbs measures

Pieter Allaart, Johannes Jaerisch

Pointwise Hölder exponents describe the degree of regularity of a function near a point. For a function $f : R \to R$ , a number $α > 0$ and a point $t_{0} \in R$ ,…

math.CA2025

The dimension of random subsets of self-similar sets generated by branching random walk

Pieter Allaart, Lauritz Streck

Given a self-similar set $Λ$ that is the attractor of an iterated function system (IFS) ${f_{1}, \dots, f_{N}}$ , consider the following method for constructing a random subset of $Λ$ :…

math.DS2024

The $β$ -transformation with a hole at $0$ : the general case

Pieter Allaart, Derong Kong

Given $β > 1$ , let $T_{β}$ be the $β$ -transformation on the unit circle $[0, 1)$ , defined by $T_{β} (x) = β x - ⌊ β x ⌋$ . For each $t \in [0, 1)$ let $K_{β} (t)$ be the survivor set consist…

Equality of Hölder exponents for distribution functions of Gibbs measures

The dimension of random subsets of self-similar sets generated by branching random walk

The β-transformation with a hole at 0: the general case

The $β$ -transformation with a hole at $0$ : the general case