44 citations · 231 across the 34 of their papers we have counts for
9 papers · 1 filter
The Hausdorff measure version of Gallagher's theorem -- closing the gap and beyond
Mumtaz Hussain, David Simmons
In this paper we prove an upper bound on the "size" of the set of multiplicatively -approximable points in for in terms of -dimensional Hausdorff measure.…
Random walks on homogeneous spaces and diophantine approximation on fractals
David Simmons, Barak Weiss
We extend results of Y. Benoist and J.-F. Quint concerning random walks on homogeneous spaces of simple Lie groups to the case where the measure defining the random walk generates…
Diophantine approximation in Kleinian groups: singular, extremal, and bad limit points
Victor Beresnevich, Anish Ghosh, David Simmons +1
The overall aim of this note is to initiate a "manifold" theory for metric Diophantine approximation on the limit sets of Kleinian groups. We investigate the notions of singular an…
Badly approximable points on self-affine sponges and the lower Assouad dimension
Tushar Das, Lior Fishman, David Simmons +1
We highlight a connection between Diophantine approximation and the lower Assouad dimension by using information about the latter to show that the Hausdorff dimension of the set of…
Uniformly de Bruijn sequences and symbolic Diophantine approximation on fractals
Lior Fishman, Keith Merrill, David Simmons
Intrinsic Diophantine approximation on fractals, such as the Cantor ternary set, was undoubtedly motivated by questions asked by K. Mahler (1984). One of the main goals of this pap…
The Hausdorff and dynamical dimensions of self-affine sponges: a dimension gap result
Tushar Das, David Simmons
We construct a self-affine sponge in whose dynamical dimension, i.e. the supremum of the Hausdorff dimensions of its invariant measures, is strictly less than its Hau…