46 citations · 268 across the 58 of their papers we have counts for
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The Fourier spectrum and sumset type problems
Jonathan M. Fraser
We introduce and study the \emph{Fourier spectrum} which is a continuously parametrised family of dimensions living between the Fourier dimension and the Hausdorff dimension for bo…
Assouad-type Dimensions of Overlapping Self-affine Sets
Jonathan M. Fraser, Alex Rutar
We study the Assouad and quasi-Assoaud dimensions of dominated rectangular self-affine sets in the plane. In contrast to previous work on the dimension theory of self-affine sets,…
Assouad type dimensions of infinitely generated self-conformal sets
Amlan Banaji, Jonathan M. Fraser
We study the dimension theory of limit sets of iterated function systems consisting of a countably infinite number of conformal contractions. Our focus is on the Assouad type dimen…
The Assouad spectrum of Kleinian limit sets and Patterson-Sullivan measure
Jonathan M. Fraser, Liam Stuart
The Assouad dimension of the limit set of a geometrically finite Kleinian group with parabolics may exceed the Hausdorff and box dimensions. The Assouad \emph{spectrum} is a contin…
The Assouad dimension of self-affine measures on sponges
Jonathan M. Fraser, István Kolossváry
We derive upper and lower bounds for the Assouad and lower dimensions of self-affine measures in generated by diagonal matrices and satisfying suitable separation co…
Assouad type dimensions of parabolic Julia sets
Jonathan M. Fraser, Liam Stuart
We prove that the Assouad dimension of a parabolic Julia set is where is the Hausdorff dimension of the Julia set. Since may be strictly less than 1, this pro…
Refined horoball counting and conformal measure for Kleinian group actions
Jonathan M. Fraser, Liam Stuart
Parabolic fixed points form a countable dense subset of the limit set of a non-elementary geometrically finite Kleinian group with at least one parabolic element. Given such a grou…
Parabolic carpets
Jonathan M Fraser, Natalia Jurga
We introduce and study a family of non-conformal and non-uniformly contracting iterated function systems. We refer to the attractors of such systems as parabolic carpets. Roughly s…