40 citations · 176 across the 31 of their papers we have counts for
35 papers
A dichotomy on the self-similarity of graph-directed attractors
Kenneth J. Falconer, Jiaxin Hu, Junda Zhang
This paper seeks conditions that ensure that the attractor of a graph directed iterated function system (GD-IFS) cannot be realised as the attractor of a standard iterated function…
Box-counting dimension in one-dimensional random geometry of multiplicative cascades
Kenneth J. Falconer, Sascha Troscheit
We investigate the box-counting dimension of the image of a set under a random multiplicative cascade function . The corresponding result for Hausdorff di…
Intermediate dimension of images of sequences under fractional Brownian motion
Kenneth J. Falconer
We show that the almost sure -intermediate dimension of the image of the set under index- fractional Brownian motion is $\f…
Intersections of thick compact sets in
Kenneth Falconer, Alexia Yavicoli
We introduce a definition of thickness in and obtain a lower bound for the Hausdorff dimension of the intersection of finitely or countably many thick compact sets u…
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…
The density of sets containing large similar copies of finite sets
Kenneth Falconer, Vjekoslav Kovač, Alexia Yavicoli
We prove that if () is a Lebesgue-measurable set with density larger than , then contains similar copies of every -point…