Jonathan M. Fraser

collaborators

6 papers

math.DS2025

Dimensions of orbital sets in complex dynamics

Jonathan M Fraser, Yunlong Xu

Let $E$ be a non-empty compact subset of the Riemann sphere and $T$ be a rational map of degree at least two. We study the associated \emph{orbital set}, that is, the backwards o…

math.CA2025

Hausdorff dimension of restricted Kakeya sets

Jonathan M. Fraser, Lijian Yang

A Kakeya set in $R^{n}$ is a compact set that contains a unit line segment $I_{e}$ in each direction $e \in S^{n - 1}$ . The Kakeya conjecture states that any Kakeya set in $\mat…

math.MG2025

Sobolev and quasiconformal distortion of intermediate dimension with applications to conformal dimension

Jonathan M. Fraser, Jeremy T. Tyson

We study the distortion of intermediate dimension under supercritical Sobolev mappings and also under quasiconformal or quasisymmetric homeomorphisms. In particular, we extend to t…

math.CA2024

On variants of the Furstenberg set problem

Jonathan M. Fraser

Given an integer $d \geq 2$ , $s \in (0, 1]$ , and $t \in [0, 2 (d - 1)]$ , suppose a set $X$ in $R^{d}$ has the following property: there is a collection of lines of packing dimens…

math.DS2024

Inhomogeneous attractors and box dimension

Jonathan M. Fraser

Iterated function systems (IFSs) are one of the most important tools for building examples of fractal sets exhibiting some kind of `approximate self-similarity'. Examples include s…

math.DS2024

Assouad spectrum of Gatzouras-Lalley carpets

Amlan Banaji, Jonathan M. Fraser, István Kolossváry +1

We study the fine local scaling properties of a class of self-affine fractal sets called Gatzouras-Lalley carpets. More precisely, we establish a formula for the Assouad spectrum o…