46 citations · 268 across the 58 of their papers we have counts for
7 papers · 1 filter
Quantifying inhomogeneity in fractal sets
Jonathan M. Fraser, Mike Todd
An inhomogeneous fractal set is one which exhibits different scaling behaviour at different points. The Assouad dimension of a set is a quantity which finds the `most difficult loc…
Inhomogeneous self-similar sets with overlaps
Simon Baker, Jonathan M. Fraser, András Máthé
It is known that if the underlying iterated function system satisfies the open set condition, then the upper box dimension of an inhomogeneous self-similar set is the maximum of th…
The Assouad dimensions of projections of planar sets
Jonathan M. Fraser, Tuomas Orponen
We consider the Assouad dimensions of orthogonal projections of planar sets onto lines. Our investigation covers both general and self-similar sets. For general sets, the main resu…
Assouad type dimensions for self-affine sponges
Jonathan M. Fraser, Douglas C. Howroyd
We study the Assouad and lower dimensions of self-affine sponges; the higher dimensional analogue of the planar self-affine carpets of Bedford and McMullen. Our techniques involve…
On the Fourier analytic structure of the Brownian graph
Jonathan M. Fraser, Tuomas Sahlsten
In a previous article (\textit{Int. Math. Res. Not.} 2014, 2730--2745) T. Orponen and the authors proved that the Fourier dimension of the graph of any real-valued function on $\ma…
Uniform scaling limits for ergodic measures
Jonathan M. Fraser, Mark Pollicott
We prove that ergodic measures on one-sided shift spaces are uniformly scaling in the sense of Gavish. That is, given a shift ergodic measure we prove that at almost every point th…