46 citations · 268 across the 58 of their papers we have counts for
10 papers · 1 filter
Box dimensions of -invariant sets
Jonathan M. Fraser, Natalia Jurga
We study the box dimensions of sets invariant under the toral endomorphism for integers . The basic example…
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…
The fractal structure of elliptical polynomial spirals
Stuart A. Burrell, Kenneth J. Falconer, Jonathan M. Fraser
We investigate fractal aspects of elliptical polynomial spirals; that is, planar spirals with differing polynomial rates of decay in the two axis directions. We give a full dimensi…
A new perspective on the Sullivan dictionary via Assouad type dimensions and spectra
Jonathan M. Fraser, Liam Stuart
The Sullivan dictionary provides a beautiful correspondence between Kleinian groups acting on hyperbolic space and rational maps of the extended complex plane. An especially direct…
Dimensions of the popcorn graph
Haipeng Chen, Jonathan M. Fraser, Han Yu
The 'popcorn function' isThe `popcorn function' is a well-known and important example in real analysis with many interesting features. We prove that the box dimension of the graph…
On Hölder maps and prime gaps
Haipeng Chen, Jonathan M. Fraser
Let denote the th prime, and consider the function which maps the reciprocals of the positive integers bijectively to the reciprocals of the primes. We…