4 papers
On the Marstrand projection theorem for the Assouad spectrum
Kenneth J. Falconer, Jonathan M. Fraser, Antti Käenmäki
Marstrand's projection theorem states that the Hausdorff dimension of the orthogonal projection of a Borel set in the plane onto lines is constant almost surely. This property exte…
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 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…
Applications of dimension interpolation to orthogonal projections
Jonathan M. Fraser
Dimension interpolation is a novel programme of research which attempts to unify the study of fractal dimension by considering various spectra which live in between well-studied no…