128 citations · 387 across the 40 of their papers we have counts for
5 papers · 1 filter
Equi-homogeneity, Assouad Dimension and Non-autonomous Dynamics
Alexander M. Henderson, Eric J. Olson, James C. Robinson +1
We show that self-similar sets arising from iterated function systems that satisfy the Moran open-set condition, a canonical class of fractal sets, are `equi-homogeneous'. This is…
Some results in support of the Kakeya Conjecture
Jonathan M. Fraser, Eric J. Olson, James C. Robinson
A Besicovitch set is a subset of that contains a unit line segment in every direction and the famous Kakeya conjecture states that Besicovitch sets should have full dimensio…
Generalised Cantor sets and the dimension of products
Eric J. Olson, James C. Robinson, Nicholas Sharples
In this paper we consider the relationship between the Assouad and box-counting dimension and how both behave under the operation of taking products. We introduce the notion of `eq…
On the Assouad dimension of self-similar sets with overlaps
Jonathan. M. Fraser, Alexander. M. Henderson, Eric J. Olson +1
It is known that, unlike the Hausdorff dimension, the Assouad dimension of a self-similar set can exceed the similarity dimension if there are overlaps in the construction. Our mai…
Minimal Periods for Ordinary Differential Equations in Strictly Convex Banach Spaces and Explicit Bounds for some l^p-Spaces
Michaela A. C. Nieuwenhuis, James C. Robinson, Stefan Steinerberger
Let x(t) be a non-constant T-periodic solution to the ordinary differential equation x'= f(x) in a Banach space X where f is assumed to be Lipschitz continuous with constant L. The…