44 citations · 197 across the 17 of their papers we have counts for
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math.DS2016★ 10 cited
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…
math.DS2016★ 33 cited
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…
math.NT2016★ 6 cited
Badly approximable vectors and fractals defined by conformal dynamical systems
Tushar Das, Lior Fishman, David Simmons +1
We prove that if is the limit set of an irreducible conformal iterated function system (with either finite or countably infinite alphabet), then the badly approximable vectors…