44 citations · 231 across the 34 of their papers we have counts for
55 papers
Generalised Hausdorff measure of sets of Dirichlet non-improvable matrices in higher dimensions
Ayreena Bakhtawar, David Simmons
Let be a nonincreasing function. A pair where is a real matrix and is said to be $ψ…
Dynamical Borel-Cantelli lemma for recurrence theory
Mumtaz Hussain, Bing Li, David Simmons +1
We study the dynamical Borel-Cantelli lemma for recurrence sets in a measure preserving dynamical system with a compatible metric . We prove that, under some regular…
Regularity of Almost-Minimizers of Hölder-Coefficient Surface Energies
David Simmons
We study almost-minimizers of anisotropic surface energies defined by a Hölder continuous matrix of coefficients acting on the unit normal direction to the surface. In this general…
Hausdorff dimensions of perturbations of a conformal iterated function system via thermodynamic formalism
Tushar Das, Lior Fishman, David Simmons +1
We consider small perturbations of a conformal iterated function system (CIFS) produced by either adding or removing some generators with small derivative from the original. We est…
The Measure Game
Logan Crone, Lior Fishman, Stephen Jackson +2
We study a game first introduced by Martin (actually we use a slight variation of this game) which plays a role for measure analogous to the Banach-Mazur game for category. We firs…
On the dimension spectra of infinite iterated function systems
Tushar Das, David Simmons
The dimension spectrum of a conformal iterated function system (CIFS) is the set of all Hausdorff dimensions of its various subsystem limit sets. This brief note provides two const…