3 citations · 5 across the 4 of their papers we have counts for
5 papers
Fractal geometry of Bedford-McMullen carpets
Jonathan M. Fraser
In 1984 Bedford and McMullen independently introduced a family of self-affine sets now known as \emph{Bedford-McMullen carpets}. Their work stimulated a lot of research in the area…
-spectra of measures on planar non-conformal attractors
Kenneth J. Falconer, Jonathan M. Fraser, Lawrence D. Lee
We study the -spectrum of measures in the plane generated by certain nonlinear maps. In particular we consider attractors of iterated function systems consisting of maps whose…
Assouad dimension and fractal geometry
Jonathan M. Fraser
This is a book to be published in 2020 by Cambridge University Press (Tracts in Mathematics Series). It focuses on the Assouad dimension of sets and measures in Euclidean space, as…
Approximate arithmetic structure in large sets of integers
Jonathan M. Fraser, Han Yu
We prove that if a set is `large' in the sense of Erdős, then it approximates arbitrarily long arithmetic progressions in a strong quantitative sense. More specifically, expressing…
Interpolating between dimensions
Jonathan M. Fraser
Dimension theory lies at the heart of fractal geometry and concerns the rigorous quantification of how large a subset of a metric space is. There are many notions of dimension to c…